
Class S_£LSX1 

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FOREST VALUATION 



BY 



HERMAN HAUPT CHAPMAN, M. F. 

Harriman Professor of Forest Managetnent 
Yale University Forest School 



FIRST EDITION 

FIRST THOUSAND 



NEW YORK 
JOHN WILEY & SONS, Inc. 

London: CHAPMAN & HALL, Limited 
I915 



SH 55 \ 



Copyright, 1914, 

BY 

HERMAN HAUPT CHAPMAN 



Stanbopc flJrcss 

F. H.GILSON COMPANY 
BOSTON, U.S.A. 



DEC 16 1914 

©CI.A387957 



To 

HENRY SOLON GRAVES 

Forester 

m RECOGNITION OF THE SERVICES WHICH HE IS RENDERING TO THE 
NATION AND TO FORESTRY BY MAINTAINING A HIGH STAND- 
ARD OF EFFICIENCY AND INTEGRITY IN PUBLIC OFFICE, 
AND BY UPHOLDING BOTH THE SPIRIT AND THE 
LETTER OF NATIONAL FOREST POLICY 



PREFACE 

The term Forest Valuation, applied to this volume, covers 
only a portion of the subject of Forest Finance, which is usually 
separated into two parts, termed, respectively, Valuation and 
Statics. Valuation deals with the determination of the value of 
standing timber, both mature and immature, and of forest soil, 
and the forest as a whole. Forest Statics deals with the 
comparison of financial results obtained in forestry with those 
yielded by other enterprises, and compares the relative merits 
of different methods of treating the forest. This subject is dis- 
cussed in Chapter VIII. Since Forest Valuation includes the 
greater portion of the text, and this term is more familiar to 
American foresters, it has been adopted as the title, in place of 
the more comprehensive term. Forest Finance. 

The literature of Forest Finance is largely of German origin, 
and has been developed in the latter half of the nineteenth 
century, by numerous German and French authorities. The 
standard English text is found in ''Forest Management," by 
Sir William Schlich, Vol. Ill, Part II, Forest Valuation.* This 
author follows the continental treatment of the subject. In 
1909, a pamphlet on " Forest Finance " was published by C. A, 
Schenck, Ph.D., Forester to the Biltmore estate,! which gives a 
synopsis or outline of a series of lectures on the subject. Dr. 
Schenck's treatment is thoroughly American and contains valu- 
able suggestions for the advanced student of Forest Finance. 

Unfortunately, neither of these publications treats the subject 
in a sufficiently elementary manner to serve as a textbook for 
students of forestry or for persons desiring information who are 
not already thoroughly familiar with the economic and mathe- 

* Fourth Edition, Revised. Bradbury, .\gnew & Co., Ld., 10 Bouverie St., 
London, 1911. 

t Inland Press, Asheville, N. C, 1909. 



VI PREFACE 

matical principles on which the theory of Forest Finance is 
based. Forest Valuation deals with periods of time far longer 
than are considered in most financial calculations. The theory 
and application of compound interest as a mathematical means 
of determining value needs a more complete exposition than is 
usually given even in courses in economics, before the signifi- 
cance of the methods taught in valuation can be grasped. Forest 
Valuation, while disguised as a mathematical science, is in reality 
the application of broad economic principles, equally serviceable 
in the determination of all values. 

In order that the reader who is not thoroughly grounded in 
economics may readily grasp these principles as applied in 
actual Forest Valuation, Chapters I to IV have been devoted 
to a summary of economic subjects and tenets, with especial 
emphasis on interest. The ideas set forth follow the mathematical 
methods used by many economists and expressed by Prof. Irving 
Fisher of Yale University.* These chapters will serve the 
additional purpose of stating the economic basis upon which 
the discussion of disputed questions in the text is made to rest, 
and will enable students who disagree with any of these funda- 
mental definitions or principles to substitute those of other 
authorities more to their liking. 

To the general reader and even to the student, the use of 
formulae as a means of expressing economic relations is apt to 
convey the impression that the subject is a difficult one to grasp. 
The effort to attach the proper significance to symbols must 
precede that required to reach the mathematical solution. The 
first difficulty is lessened by the consistent use of symbols to 
which a definite meaning is attached. An entire chapter (V) 
has been devoted to an explanation of the derivation of the 
formulae of compound interest. A further difiiculty has arisen 
in the past, because the methods of treatment of the subject of 
Forest Valuation bore no relation to, and were apparently wholly 
at variance with, the customs and principles of business account- 
ing. An effort has been made in the present volume to indicate 

* "Elementary Principles of Economics." The Macmillan Company, New 
York, July, 1912. 



PREFACE Vll 

r 

these relations, and enable accountants and business men to 
harmonize the methods used in computing cost and value for 
forest property, with the forms and ideas with which they are 
familiar. 

Lastly, the emphasis has been shifted from the determination 
of expectation value of forest soil, so conspicuous a feature of 
European Forest Finance, to the consideration of stumpage 
values, sale values, damages, and other subjects of greater prac- 
tical interest in this country. 

The volume is intended primarily for use as a textbook. 
But in recognition of the frequent need for information on such 
subjects as damages, stumpage values and costs of forest pro- 
duction, a consistent effort has been made to treat the entire 
subject in a manner that may be readily grasped by the average 
reader, without previous preparation or study. 

No problems have been included in the text. These should 
be supplied by instructors to suit the local economic conditions. 
The table of logaritl\ms has been included for convenience, to 
enable the student to familiarize himself with its use in solving 
problems of valuation. 

Acknowledgment is made to Prof. Fred R. Fairchild of Yale 
University for review and criticism of Chapter X on Taxation, 
to Mr. J. E. Glass, accountant for John Wiley & Sons, Inc., 
for suggestions regarding forms for forestry accounts shown in 
Chapter VIII, and to my colleagues on the faculty of the Yale 
Forest School for valuable suggestions and assistance. 

HERMAN H. CHAPMAN. 

New Haven, Conn., 
October 22, 1914. 



CONTENTS 



CHAPTER I 

VALUES 
Article Page 

1. Wealth and Property i 

2. The Standard of Value i 

3. Prices 2 

4. Values 2 

5. Demand 2 

6. Effort or Outlay 3 

7. Ownership 3 

8. Prices of Finished Products 4 

9. Prices of Raw Materials and Natural Resources 5 

10. Future Costs S 

11. The Element of Time in Values 6 

12. Capital 6 

13. The Capitalist 7 

14. Interest 7 

15. Discount 8 

16. Compound Interest and Discount 8 

17. Sale Value 9 

18. Appraised Value 10 



CHAPTER II 
OUTLAY AND INCOME 

19. Proprietary Accounts versus Specific or Valuation Accounts 11 

20. Capital Accounts 11 

21. Outlay and Income Accounts 12 

22. Investments versus Expenses 13 

23. The Relation in Time between Outlay and Income 14 

24. The Total Investment 14 

25. Cost Accounts 16 

26. Income 16 

27. The Economic Opportunity 16 

28. The Business Venture 17 

29. Exchange 17 

30. Disposition of Income 17 

31. Returns on Capital 18 

ix 



X CONTENTS 

Article Page 

32. Interest versus Dividends 18 

SS. Profits 19 

34. Wages versus Profits 19 



CHAPTER III 
INTEREST 

35. The Problem of Interest 21 

36. Interest as a Cost 21 

37. Interest as Income 22 

38. The " Rate of Interest " 22 

39. The Profits of the Undertaking 23 

40. Annual Profits 23 

41. Deferred Profits 23 

42. Income versus Profits 24 

43. Influences Determining the "Rate of Interest" 26 

44. The Influence of Personahty on the Rate of Interest 26 

45. Risk and Expense 27 

46. Fluctuating Value of Money 27 

47. The Rate of Interest for Business Investments 28 

48. The Effect of Deferred Income upon the Rate of Interest 28 

49. Comparison of Results of Simple and Compound Interest 28 

50. Limitation of Opportunity 29 

51. Effect of the Rate of Interest upon. Accumulations of Compound 

Interest 30 

52. The Rate of Interest in Forest Investments 32 

53. Comparison of Interest Rates in Forestry with Other Investments. ... $$ 



CHAPTER IV 
VALUATION OF ASSETS 

54. Valuation Accounts 35 

55. The Inventory 35 

56. Cost as a Basis of Value 35 

57. Expenses and Interest versus Value 35 

58. Essential Difference between Cost and Value 37 

59. Sale Value as a Basis of Value 37 

60. Appraisal of Value 38 

61. Future Income as the Basis of Value 38 

62. Capital Value or Expectation Value 39 

63. Future Prices and Values 41 

64. Future Expenses 41 

65. The Time Element in Capital Values 42 

66. Effect of Rate of Interest on Capital Values 42 

67. Uncertainty of Capital Value 43 

68. Independence of Capital Value and Past Outlay or Cost 44 



CONTENTS Xi 

Article Page 

69. Effect of Capital Value on Sale Value 44 

70. Effect of Capital Value upon Appraised Value 45 

71. Inflation of Capital Values 45 

72. The Regulation of Capitalization 46 

73. The Problem of the Balance Sheet 46 



CHAPTER V 
FORMUL-S: OF COMPOUND INTEREST 

74. The Discount Factor 53 

75. Rentals 53 

76. Future Value or Cost of Single Sums 53 

77. Present, Expectation, or Capital Value of Future Sums 54 

78. Use of Logarithms and Tables 55 

79. Future Value of Temporary Annual Rentals 56 

80. Formulae for Geometric Series 57 

81. Present, Expectation, or Capital Value of Temporary Annual Rentals 58 

82. Future Value of Temporary Intermittent Rentals Due First at n Years, 

and t Times at Intervals of n Years Thereafter 59 

83. Present, Expectation, or Capital Value of Temporary Intermittent 

Rentals, Due First at n Years, and t Times at Intervals of n Years 
Thereafter 60 

84. Future Value of Temporary Intermittent Rentals, Due First in a Years, 

and t Times at Intervals of n Years Thereafter 60 

85. Present, Expectation, or Capital Value of Temporary Intermittent 

Rentals, Due First in a Years, and / Times at Intervals of n Years 
Thereafter 61 

86. Present, Expectation, or Capital Value of Perpetual Rentals 62 

87. Relation between Future Value of Temporary Annual Rentals, and 

Present, or Capital, Value of Same 65 

88. Conversion of Intermittent into Annual Rentals 65 

89. The Ratio of Income or Earnings 66 



CHAPTER VI 
INVESTMENTS AND COSTS IN FOREST PRODUCTION 

90. The Business of Forest Production versus Lumbering 68 

91. Proprietary Accounts in Forestry 69 

92. Cost Accounts in Forestry 70 

93. Investments, or Permanent Outlay 71 

94. Expenses, or Temporary Outlay in Forestry 71 

95. Land 71 

96. Standing Timber 72 

97. Permanent Improvements and Equipment 73 

98. Roads and Transportation Systems 73 



xil CONTENTS 

Article Page 

99. Silvicultural Operations 74 

100. Protection Expenses 74 

loi. Administrative Expenses 75 

102. Taxes and Insurance 76 

103. Interest Charges 76 

104. Classification of Costs in Forest Production 76 

105. Calculation of Total or Final Costs 77 

106. Total Cost of Investments in Standing Timber 79 

107. Costs of Forestry Compared with Destructive Lumbering 81 

108. Cost of Many-aged Forests 83 

109. Cost of Producing a Normal Forest 84 



CHAPTER VII 
THE VALUATION OF FORESTS 



no 



Valuation Accounts in Forestry 85 

111. Income as the Basis of Value of Forests 85 

112. Value of Forest Property for Destructive Lumbering 86 

113. Value of Forest Property for Continuous Forest Production 88 

114. Value of a Forest of Even Age Just Previous to Cutting 89 

115. Value of an Even-aged Forest for Any Year 90 

116. Value of Forest Soil 92 

117. Value of Many-aged Forests Producing Regular Income 96 

118. Value of Many-aged Forests Producing Irregular Income 97 

119. Value of Timber Separate from Land 98 



CHAPTER VIII 
FOREST STATICS — THE BALANCE SHEET — PROFITS 

120. Determining the Profits of an Investment 100 

121. The Rate of Interest in its Relation to Profits 104 

122. Profits in Destructive Lumbering . . . . , 105 

123. Profits on a Stand of Timber 106 

124. Anticipated Profits on Young Timber 106 

125. Profits from Continuous Forest Production 107 

126. Anticipation of Continuous Profits 107 

127. Profits Expressed as Soil Values 108 

128. Profits Expressed as a Ratio of Income to Capital no 

129. Earning Power of Capital Invested in Forest Production in 

130. The Relative Importance of Profits in Private versus Public Forestry. 115 

131. Forms for Specific Accounts in Forestry 117 

132. Forms for Economic Accounts in Forestry 119 



CONTENTS XUl 



CHAPTER rX 



THE APPRAISAL OF DAMAGES 

Article Page 

133. Principles Underlying Appraisal of Damages 120 

134. Elements of Damage to Forest Property 122 

135. Physical Separation of Timber from Soil 122 

136. Separation of Value of Timber from Value of Soil 123 

137. A Basis of Damages: Cost of Replacement 126 

138. A Basis of Damages: Sale Value 128 

139. A Basis of Damages: Expectation or Capital Value 129 

140. Damage to Merchantable Timber 131 

141. Damage to Immature Timber: Partial Loss 132 

142. Damage to Immature Timber: Total Loss 133 

143. Damage to Forest Soil 135 

144. Damage to Single Trees 136 

145. Damage to Many-aged Stands 137 

146. Damage to Watersheds 137 

147. Esthetic Values 138 

148. Punitive Damages 139 



CHAPTER X 
FOREST TAXATION 

149. Sources of Revenue from which to pay Taxes 141 

150. Tax on Income 141 

151. Tax on Value of^Property 142 

152. Taxable Value of Property 143 

153. Effect of Taxes on Property Values 143 

154. The General Property Tax 144 

155. The Problem of Taxation for Timberlands 145 

156. Distinction between Capital and Income in Timber Property 145 

157. The Problem of Interest in Forest Taxation 146 

158. Effect of Present Condition of Forest upon Choice of Methods of 

Taxation : i47 

159. Scientific Taxation: Forest Property Tax 149 

160. Scientific Taxation: Forest Land Tax 150 

161. Comparison of Taxes on Forest Rent versus Soil Rent 151 

162. Scientific Taxation: Income or Products Tax 152 

163. Scientific Taxation: Combined Capital Tax and Income Tax 154 

164. Taxes under the General Property Tax i5S 

165. Effect of the General Property Tax on Forest Production 158 

166. Tax Reform for Forest Property 160 



xiv CONTENTS 

CHAPTER XI 

STUMPAGE VALUES 

Article Page 

167. Definition of Stumpage Value 166 

168. Sale Value of Stumpage 166 

169. Stumpage Prices 167 

170. Factors Determining Stumpage Prices 167 

171. Appraisals of Stumpage Value 169 

172. The Price Basis in Appraisals 170 

173. Depreciation 173 

174. Milling Costs and Profits 177 

175 Logging Costs and Profits 178 

176 Stumpage as a Capital Investment and as a Cost of Raw Material. . . . 180 

177 The Determination of Legitimate Profits: Overturn Methods 181 

178. The Investment Basis for Profits 184 

179. Overrun 187 

180. Stumpage Values for Different Species in Mixed Stands 188 

181. Carrying Charges versus Profits on Stumpage 191 



CHAPTER XII 
FUTURE VALUE OF FOREST PRODUCTS 

182. Factors Affecting Future Value 195 

183. The Stand: Growth in Volume 195 

184. The Stand: Improvement in Quality of Products 196 

185. Deterioration of Standing Timber 196 

186. Closeness of Utilization 197 

187. Price Levels: General Price Changes 197 

188. Price Levels: Changes in Prices of Forest Products 197 

189. Effects of Substitutes on Wood Prices 198 

190. Future Operating Costs 201 

191. Local Factors: Future Transportation Facilities 202 

192. Local Factors: Industries and Markets 203 

193. Local Factors: Future Supply of Timber 204 

194. The Rate of Increase in Stumpage Value 204 

195. Increasing Future Values as a Basis of Appraisals 206 

196. Revision of Stumpage Values in Long-term Contracts 207 

CHAPTER XIII 
RISKS 

197. Risks versus the Rate of Interest in Forestry 208 

198. The Nature of Risks in Forestry 208 

199. The Gauging of Risks 209 

200. Physical Risks : Fire 209 

201. Wind 210 



CONTENTS XV 

Article Page 

202. Insects 211 

203. Fungous Diseases 2ir 

204. Climatic Injuries 211 

205. Injurious Fumes 212 

206. Moral Risks: Trespass 212 

207. Fire 212 

208. Financial Risks 212 

209. Control of Risks: Insurance 213 

210. Public Measures 213 

211. Private Measures 214 

212. Effect of Risks on the Business of Forest Production 214 

CHAPTER XIV 
FIELD APPRAISALS OF TIMBER STUMPAGE 

213. The Scope of Field Appraisals 216 

214. Timber Reconnaissance: The Map 217 

215. Estimation of Standing Timber 218 

216. Log Rules 218 

217. Closeness of Utilization as Afifecting Timber Estimates 219 

218. Field Methods of Timber Estimating 219 

219. Strip Methods 220 

220. Errors in These Methods 220 

221. Types 221 

222. Correction Factors 221 

223. Quality of Timber 222 

224. Reports 222 



CHAPTER XV 

COMPARISON OF FOREST VALUES WITH AGRICULTURAL 

VALUES 

225. Agricultural Soils 226 

226. Quality of Soil 226 

227. Slope 226 

228. Climate 226 

229. Water 227 

230. Personal Factors 227 

231. Economic Factors 227 

232. Comparison of Agriculture with Forestry as a Source of Livelihood . . . 227 

233. Non-agricultural Soils 228 

234. Exploitation of Land Purchasers 229 

235. Land Classification 229 

236. Basis of Comparison of Agricultural and Forest Values of Land 229 

237. Expectation Value of Agricultural Land 230 

238. Sale Value of Agricultural Land 230 



XVI CONTENTS 

Article Page 

239. Timber as an "Agricultural" Value 230 

240. Stump Land versus Cleared Land 231 

241. Cost of Clearing Stump Lands 232 

242. Sale Value of Stump Lands 232 

243. Summary of Elements of Value for Forest Land 233 

244. Value of Young Timber as a Part of the Value of Forest Soil 234 

245. Sale Value of Forest Property 235 

246. Discrimination against Forest Values 236 

247. Discrimination in Favor of Forest Values 236 

248. Results, when Values of Bare Land are Compared 237 

249. Results, when Full Value of Property is used in Comparison 237 

250. National Forest Policy in Land Classification 238 

251. Reciprocal Values in Forestry and Agriculture 239 

Appendix 240 

Summary of Formulae of Compound Interest 240 

Definitions of Symbols 241 

Summary of Formiilae in Forest Valuation 243 

Costs 243 

Values 244 

Profits 246 

Interest Earned 246 

Damages 247 

Depreciation 247 

Geometric Series 248 

Stumpage Values 248 

Compound Interest Tables: 

Explanation 249 

Table VI 250 

Tables of Logarithms of Numbers 265 



FOREST VALUATION 



CHAPTER I 
VALUES 

1. Wealth and Property. — Wealth is defined as material 
objects owned by human beings. Forest wealth consists of 
forest land and its resources, principally trees, but including all 
other materials such as forage and game. 

Property is the right represented by ownership, and not the 
material object itself. The benefits derived from wealth make 
its ownership desirable. The right to enjoy these benefits is 
indicated by the term property. The satisfactions to be derived 
from ownership of forest property, aside from the pleasures of 
sport and recreation, take the form of money income from the 
sale of forest products. 

2. The Standard of Value. — Value is an expression of the 
relative desirability of different forms of wealth or property in 
terms of a common standard. The form of wealth accepted 
as this standard is termed money, and is exchangeable for all 
other kinds of wealth or property. The present standard in 
this country is gold. The value of money itself can only be 
measured by its purchasing power, which means its relative 
desirability compared with other goods. Changes in the quan- 
tity and rapidity of circulation of money cause its purchasing 
power or value to fluctuate, and a decline in value of money 
means higher prices for all other property. Prices in the im- 
mediate past have risen. If continued, this tendency will be 
a conservative factor in the valuation of forests; while in con- 
trast, such property as long term bonds will tend to fall in value, 
because it is redeemable in money. 



2 FOREST VALUATION 

3. Prices. — A price, when expressed in terms of the common 
standard of value, is the amount of money accepted in exchange 
for a unit of goods. Until the actual exchange is consummated 
the price is not definitely established, but exists merely as an 
appraisal or opinion in the mind of the prospective buyer or the 
present owner. Prices resulting from exchanges are agreements 
between two persons as to the value of a unit of property. 
Market prices originate in centers of trade and form the basis 
of numerous transactions. Prices are therefore of human and 
mental origin and are established by economic causes which 
influence the opinions of the majority of purchasers and sellers. 
While in the main, prices move in response to supply and demand, 
yet the fluctuations in price of certain forms of property, such 
as real estate and stocks, demonstrate that it is possible to 
create market prices either higher or lower than circumstances 
justify, by influencing general or pubHc opinion through opti- 
mism, misrepresentation, or concealment of facts. 

4. Values. — Value may be defined as the price of a given 
unit of wealth, multiplied by the quantity or number of units. 
Thus the value of a given quantity of cordwood is the price per 
cord multiplied by the number of cords on hand. This defini- 
tion holds good if prices are accepted as the final standard of 
value. For finished products, especially staple commodities, 
actual prices established by exchanges may be taken as deter- 
mining value. But for forms of goods in an unfinished state, 
or for productive wealth, such as land or growing timber, prices 
furnish only contributory evidence of value, which in many 
instances is entirely misleading. The very fact that prices for 
finished products are the basis of value indicates that the value 
of productive property must be derived from that of its products. 
Ignorance of the true productiveness of property, and of the 
mathematical relation between this income and the value of 
the property, is the principal cause of divergence between current 
prices and true value for such forms of wealth as forest lands 
and young timber. 

5. Demand. — The influences which determine prices are 
twofold, corresponding roughly to the two persons concerned 



VALUES 3 

in the transfer. Demand, or the need of the purchaser, is 
weighed against outlay or effort on the part of the owner. The 
necessities and desires of the human mind and body, such as 
food, clothing and shelter, create the demand for any form of 
material wealth. Civilized society differs from primitive condi- 
tions by the greater extent and complexity of its needs. Values 
are thus created which have no existence among savages. This 
fact is strikingly illustrated by the history of the timberlands 
belonging to Indian tribes. To the American Indians the pine 
timber was of no value whatever, and their use of the forest was 
confined to its game and fish, the destruction of which they 
deeply resented. Title to much of this forest land was given 
to various tribes by the government. This timber soon came 
to have a high value to the white population, and the Indians 
were either defrauded of values which they had failed to appre- 
ciate, or found themselves enriched by these same values which 
they had no part in creating. 

6. Effort or Outlay. — Human demand or needs would not 
alone create values. Materials indispensable to life remain 
without value when they can be obtained without effort. Prop- 
erty which is worth owning has cost the original owner some 
effort either for its acquisition or improvement. This influences 
his idea of its value. A prospective purchaser gauges his price 
by the possibility of securing a similar article through his own 
efforts. The supply of finished products is greatly influenced 
by cost of production. 

7. Ownership. — The whole structure of values rests on the 
institution of private property, for without the right of owner- 
ship there could be no measurable value. In a primitive state 
of society each individual is able, after a fashion, to supply his 
own needs. But with specialization and division of labor, pro- 
ducers of most forms of wealth need very little of it themselves 
and must sell it, while the purchasers would be unable to produce 
for themselves the small quantities they need at anything like the 
price at which it is sold. Purchasers therefore seek the lowest 
price, while owners, in order to dispose of their surplus or to in- 
crease their output, often underbid one another. With unlimited 



4 FOREST VALUATION 

competition among producers, prices tend frequently to fall 
below the cost of production. But where the supply of an 
article of wealth is limited, and no satisfactory substitutes are 
available, the owner may demand and receive exorbitant prices, 
profiting by the needs of the consumers. In such cases there 
is no relation between prices and cost of production. Famine 
prices for food are obtained in times of flood or temporary 
scarcity. Elements which tend to increase the advantage of 
the owner and the margin between costs and value are: first, 
absence or monopoly of transportation facilities; second, the 
elimination of competition, by monopoly of the sources of supply 
or manufacture; and third, monopoly of markets. In some 
lines of production this control, through the power incidental to 
ownership, has curtailed production and has had a marked effect 
upon prices. Combinations or trade agreements may bring 
about this result. This condition is manifested in the lumber 
trade chiefly by the maintenance of local retail prices regard- 
less of the fluctuations of the general lumber market. Rail 
competition will prevent the possibility of combination on 
the part of manufacturers of lumber for an indefinite 
period. 

8. Prices of Finished Products. — Since the immediate 
needs of persons and their satisfaction from material sources 
create value, it follows (§ 4) that the prices established for goods 
ready for immediate consumption or use are the basis or source 
of value for all forms of wealth. Both needs and prices are a 
matter of to-day. The element of cost, in so far as it affects 
prices, is completed in the final product. Purchasers and venders 
are separated into two classes with sharply divided interests, 
the one obliged to buy, the other with no recourse but even- 
tually to sell. Under such circumstances prices absolutely 
determine value. The price of lumber, ties, cordwood and other 
forest products depends to as great an extent upon the demand 
and markets as upon the cost of production, and in periods of 
depression, lumber frequently sells for less than this cost. But 
whatever the conditions, these market prices determine the 
value of forest products. 



VALUES 5 

9. Prices of Raw Materials and Natural Resources. — Raw 

materials, such as pig iron or wool, are valuable to owner or 
purchaser only for further manufacture. A lowering of the cost 
of production makes it possible to sell these products more 
cheaply, but scarcity and increased demand may completely 
offset this tendency and cause higher prices. The value of raw 
products is derived directly from the price of finished goods. 
Logs and timber stumpage derive their value from retail and 
wholesale lumber prices. Property used for production is valu- 
able only because of its products. The value of agricultural 
land depends upon its adaptability for certain kinds of farm 
crops, and upon the prices these crops will bring. The market 
price for lumber is the source of value for forest land. 

Prices for land should therefore depend entirely upon future 
income derived from its products or use. Costs already incurred 
for clearing or improvements are not considered, for if land is 
worth either more or less than the cost of clearing, its value 
and not its cost will fix its price. If two grades of land, one 
good and one poor, cost the same amount for clearing, they 
will still sell for entirely different prices. Both the owner and 
the purchaser of land desire it merely for its future use and 
income. Sale is seldom forced, since the owner can probably 
make a living by developing and using the property. The price 
paid for such property thus depends upon expected income whose 
value is determined by the prices of the products which the land 
yields. 

10, Future Costs. — While costs already incurred do not 
determine the value of productive wealth, future costs which 
intervene between the present moment and the final attainment 
of income must be subtracted from the value of this income. 
If it can be shown that the future cost of obtaining income 
exceeds the future value of the income, the property itself will 
be worthless. Thus the value of standing timber is the margin 
left after subtracting from the sale value of the lumber the esti- 
mated costs of logging, manufacturing and transporting this 
lumber to market. At present prices, nearly all standing timber 
has a stumpage value, but in the past only the most accessible 



6 FOREST VALUATION 

trees had any value. Wild land or stump land may be worthless 
under present conditions, in spite of a fertile soil, if it is evident 
that the labor of clearing exceeds the discounted value of the 
income from the crops which may be raised. Most land is cleared 
at an economic loss, and there is a tendency to hold cut-over 
or stump lands at prices which greatly exceed their real value 
as reduced by the future costs of clearing. 

11. The Element of Time in Values. — As prices and values 
center upon the satisfaction of human needs in the present 
moment, the tendency is to avoid delay and reduce as far as 
possible the period which elapses between effort and satisfac- 
tion. Yet this element of time intervenes in every process of 
production. Hunting and fishing supply food within a very 
short period, which explains the dependence placed upon this 
source of living by primitive people. In agriculture, the period 
which must elapse between effort and satisfaction is extended 
to cover the crop season, and enough surplus must be produced 
to last a year. Modern engineering, illustrated by railroad 
construction, requires still greater delay before any use or income 
can be derived from the property. If the laborers who construct 
such works were also the owners, and dependent for their living 
upon the receipts from freight and passenger service, they 
would starve long before the completion of the road. The 
development of civilization is marked by the lengthening of the 
time intervening between the inception of undertakings and 
the final realization of income. This time element must always 
be considered in the determination of present values. 

12. Capital. — Men must live while engaged in production, 
and they are enabled to undertake enterprises requiring time, 
only when they have enough goods stored up to last them until 
their completion. The wealth with which to supply them con- 
sists of food, clothing and dwellings, back of which are factories, 
raw products and land. The amount of energy that can be 
diverted from immediate production of food to the task of 
clearing unproductive land or constructing other improvements 
depends upon the surplus wealth available for these purposes. 
A poor man works a lifetime to clear up a wooded farm and at 



VALUES 7 

first must earn wages by outside labor in order to live. But a 
person possessed of a few thousand dollars or its equivalent can 
hire this work done and accomplish it in a short time. 

The term capital is used to signify a stock of wealth existing 
,at a given instant of time, and therefore available for future 
use. All wealth is capital. Efforts to separate wealth into 
classes, such as that which is intended for consumption, and that 
used for the production of other wealth, lead to confusion. It 
is immaterial whether a man's capital is in the form of food, 
buildings, land or money. He will endeavor to secure by ex- 
change a proper balance between the different kinds of capital 
he possesses. The exchange of wheat for money, its reserva- 
tion for seed or its conversion into flour does not alter its status 
as capital. 

13. The Capitalist. — With sufficient capital a man is not 
only free from immediate personal wants but by employment 
and the payment of wages, can provide for the daily wants of 
others. On this basis all modern business enterprises are con- 
ducted. The time needed in constructive works may be lessened 
by increasing the number of persons employed and the capital 
expended, but only to a limited extent. For crop production, 
and in the growing of trees, the time required cannot be appre- 
ciably reduced. Since it is only by the use of capital that any 
enterprise requiring time can be undertaken, capitahsts make 
possible the entire fabric of modern civilization, and without 
this accumulated surplus we would revert to primitive condi- 
tions. In forest production the element of time is so important 
that the trend is toward state and national forestry, for govern- 
ments represent the accumulated capital of the entire community 
and can best afford to await the maturing of timber crops by 
the slow process of growth. 

14. Interest. — The present moment is the basis for comput- 
ing and comparing all values. Although use and income, on 
which value depends, continue into the future indefinitely, 
yet no one will provide for future wants and leave present 
demands wholly unsatisfied. To every one the enjoyment of 
wealth in the present is valued more highly than at any future 



8 FOREST VALUATION 

period, and the less capital a man has the greater is his prefer- 
ence for its immediate use. This preference can be satisfied 
by borrowing. The borrower obtains the benefits he seeks 
immediately, but the lender is forced to wait until the capital 
is returned before enjoying it. For this gain in " time value," 
the borrower pays interest. Upon money loans interest is 
repaid in money, the amount paid bearing a definite relation 
to the amount borrowed and to the length of time elapsing 
before repayment. Since interest and principal are in the same 
commodity, money, the relative amount and value of the interest 
can be expressed as a per cent of the principal. This per cent 
gives the rate of interest paid or earned. The period for which this 
rate is customarily quoted is one year. If the period intended 
is less than a year the fact must be clearly stated. High rates 
of interest may be based on the month, in order to make the 
rate sound less exorbitant. 

Interest, therefore, is the price of time differences or the stand- 
ard by which the value of immediate possession and enjoyment 
of income can be determined, when compared with the value of 
the same income if its receipt is postponed to a future period. 

15. Discount. — All future values can be standardized by 
reducing them to their equivalent present value by means of 
a given rate of interest. This process of reduction is termed 
discount. The discounting of money loans or demand notes 
consists of receiving in advance the value of a sum receivable 
in the future, less the difference in value due to the time elapsing 
before this payment is due. In the same way the present value 
of all forms of property is derived by consciously or uncon- 
sciously discounting its future value which takes the form of 
future income. The process of discounting is therefore the most 
important element in the valuation of forest property. 

16. Compound Interest and Discount. — Interest upon money 
loans is due and payable either annually or at shorter intervals. 
When received it may be added to the principal at the discretion 
of the owner. It may then be loaned and will in turn earn 
interest. At the end of each period of payment, provided no 
capital has been withdrawn, and interest has been promptly 



VALUES 9 

reinvested, the total investment will have increased by an amount 
representing the interest on the total sum on hand at the begin- 
ning of the period. A sum earning interest in this manner 
increases at a compound or geometric rate. 

Should the annual interest earned be withdrawn annually, 
neither the principal nor the interest earned would increase in 
amount. Should this interest be saved but not reinvested, the 
total value of principal and accumulated interest would increase 
by the same amount annually. This is termed simple interest. 
In neither of these cases is compound interest obtained. Com- 
pound interest is paid by savings banks on deposits which remain 
untouched for periods of six months or more. 

Since the earning of interest on money, without expenditure 
or withdrawal of the earnings, is equivalent to depriving the 
owner of this capital of all use of his property for the period 
covered by the loan, the difference in value of the capital at 
the beginning and end of the period measures the money value 
of the period of waiting. When money is loaned for periods 
exceeding one year, this difference in value must be computed 
by compound interest. Any lesser sum would fall short of the 
demonstrated earning power of money capital at a given rate 
of interest. Since compound interest is thus required for money 
loans it must be accepted also as the standard of time differences 
in value for all other forms of income. 

By means of compound interest at a given rate the exact 
ratio is obtained by which present values may be converted 
into future values, or, by discount, future values may be re- 
duced to their present equivalents. When both the present 
and future values are known, a rate of compound interest may 
be found which will equalize the difference in time and convert 
the one value into the other. 

17. Sale Value. — The sale value of property is indicated 
by recent prices for similar property in the same locality. In 
the absence of actual sales it is difficult to determine present 
sale value. 

Sale values are not uniform for the same kind and quality of 
goods, even in the same locaUty, unless there is a complete 



lO FOREST VALUATION 

general knowledge of current prices and the desire to buy is 
approximately equal to the pressure for sales. Should the owner 
stand in need of money he will tend to lower prices, and vice 
versa. Forced sales for cash or to Hquidate assets are made 
at prices much below the market and establish what are termed 
wrecking values. The difference in value due to forced sales 
is greatest with property used in production or for special pur- 
poses, of which real estate is a good example. A forced sale 
of forest lands, especially of young timber with no market value, 
will seldom secure more than a fraction of the true value of 
the property. 

18. Appraised Value. — Values must frequently be estab- 
lished in the absence of sales, or as a basis for such transactions 
when previous sales are either lacking or unreliable as a standard 
of value. Instances are found in condemnation proceedings, 
in settlements for damages, and in inventories or the valuation of 
assets for purposes of determining the financial status of a busi- 
ness. The principle underlying appraisals is that the value 
to the owner, for continued ownership and use, must be deter- 
mined rather than its possible value for sale, since the owner 
must not be forced to accept a lower value than that represented 
by his use or enjoyment of the property. Appraised values, for 
this reason, frequently differ sharply from sale values, especially 
in the case of slow-moving assets. 



CHAPTER II 
OUTLAY AND INCOME 

19. Proprietary Accounts versus Specific or Valuation Ac- 
counts. — Modern accounting distinguishes two classes of 
accounts, proprietary accounts and specific or valuation accounts. 
Proprietary accounts deal with the proprietor or owner's in- 
terest, and show what his outlay has been, the resulting income 
already received and the balance which represents net capital. 
These accounts show the owner as creditor of a business venture, 
the credit representing his investments. Expenses are debited 
and income or profits credited. Such accounts normally show 
a credit balance. The credit items are the plus items of the 
account. Dealing as it does entirely with outlay and income, 
it records only actual transactions or past events. 

Specific or valuation accounts deal with the assets or goods 
for which these expenses are incurred, and from which the income 
is expected. In contrast to economic accounts, they determine 
the value of these assets, and may thus introduce elements 
derived from the future as well as the past (§ 9) . 

20. Capital Accounts. — Outlay or expenditure of capital 
is undertaken for one of two purposes. Either an exchange 
is effected by which the proprietor receives goods or property 
of equal value, or the outlay is in return for services and the 
equivalent in value must be sought in the effect or results of 
such services. 

In accounting, these two classes of outlay are rigidly sepa- 
rated wherever it is possible to do so. The cost of tangible assets, 
especially of those which have a more or less durable character 
and permanent value, is entered in a capital account. This 
account is corrected by entering deductions from cost for forms 
of capital which depreciate in value and may finally become 
worthless. This factor of depreciation is common to all forms 



12 FOREST VALUATION 

of property constructed by human labor, as, for example, ma- 
chinery and buildings. The charging off of depreciation, unless 
accompanied by an appropriation of income to replace the capital 
originally expended, corresponds to a loss of capital. If re- 
placed from income, it serves to diminish the net income avail- 
able for dividends. In either case it improves the accuracy of 
the capital account. 

A capital account ought to show at any time the total amount 
of capital invested in permanent or durable assets, or the actual 
cost of these assets, whether or not there has been any sub- 
sequent increase in value. The correction for depreciation, 
which is justified by the fact of diminishing value, is in itself 
purely a matter of accounting. The amount of depreciation 
written off on the books may not, and usually does not, coincide 
exactly with the actual loss in value at the time. Should no 
account be taken of depreciation, the capital account would 
merely show that the owner had neglected to reduce the " value " 
or appropriate any of his income as replacement of capital cost. 
This is an unwise and dangerous practice, but it is optional 
with the owner except where provision for depreciation is pre- 
scribed by law for the protection of stockholders in order to 
bring the capital account into closer agreement with the actual 
value of the assets. 

21. Outlay and Income Accounts. — Outlay and income ac- 
counts, more often termed profit and loss accounts, deal first 
with the expenditures for which services are received and which 
are not therefore chargeable to capital account or regarded 
as investments. A second class of expenses usually included 
in this account is the cost of raw materials to be manufactured, 
goods to be resold, supphes to be expended in service, and fuel. 
These items represent capital and their value will be included 
in an inventory. But in most forms of business this investment 
is transitory in character, the raw materials are turned over as 
quickly as possible, and the resultant income is expected to more 
than cancel these outlays during the current year. 

Outlay and income accounts are for this reason kept as open 
accounts, to be balanced, usually, at annual intervals. Outlay 



OUTLAY AND INCOME 13 

is debited under such heads as wages, transportation, fuel, in- 
surance, light, rent, repairs, interest, taxes, supplies and cost of 
raw materials or goods. Income is credited, and in mercantile 
business consists almost wholly of receipts from sale of goods, 
to which is added incidental receipts from all other sources, 
such as rent and interest. The capital account, kept separate 
from this mass of fluctuating items of expense and income, 
is brought up to date each year by entering against it the net 
increase or decrease in actual capital resulting from the trans- 
actions of the year. Should any of the assets whose cost is 
included in the capital account be sold, the income thus re- 
ceived must be credited in the capital account to replace the cost 
of this asset. In the same manner, loss in value of capital is 
replaced through the depreciation account. Excess of sale value 
over cost of assets would be credited as profits. 

22. Investments versus Expenses. — The distinctions, or 
classifications in accounts, adopted by experience as suitable 
for modern business conducted on the basis of annual returns, 
should not be allowed to conceal the economic similarity of 
all forms of outlay and income. Outlay is undertaken with 
the sole purpose of thereby securing income. Those forms of 
outlay customarily entered in the capital account, for which 
tangible assets are received, are, it is true, regarded in the light 
of investments rather than expense by the owner. But their 
acquisition is merely the first step in securing income, and the 
culmination of the process is certain to require services or labor. 
The income will be the result of both classes of expenditure. 
That these are really identical is seen by the fact that improved 
property, purchased as capital, is largely the result of the ser- 
vices of former owners. The further expenditure for services 
by the new owner may have a sale value which a future pur- 
chaser would enter not as expense but as capital. Expenses for 
all kinds of service and supplies, instead of being an economic 
loss as must of necessity be assumed in the practice of account- 
ing, is the most important form of investment, without which 
there could be practically no income, and the capital would 
then be without value. The controlling purpose of the pro- 



14 FOREST VALUATION 

prietor is to obtain as great a ratio of income as possible for each 
unit of capital employed, whether this outlay takes the form of 
investment or subsequent expenses. 

23. The Relation in Time between Outlay and Income. — 
The element of time enters into every process of production 
(§ii). Effort normally precedes satisfaction. Money income is 
to business what the satisfaction of personal wants is to an in- 
dividual. Since outlay and effort are synonymous, it follows 
that in all forms of business, investment must precede the re- 
ceipt of income. 

This process is easily recognized in the period of installation, 
especially in such forms of business as require the completion 
of material structures. But it is equally true of the current 
business of a going concern. The receipt of income is reck- 
oned from the moment a trade is concluded. Actual payment 
may be delayed, but this is a matter of accounting. Upon the 
delivery of the goods, all expense connected with the securing 
of this income terminates, except where contracts stipulate 
future maintenance in good order for a stated period. Conse- 
quently, the wages and all other charges incurred in the securing 
of this income normally precede the final sale. The postpone- 
ment of payment of these expenses is also a mere matter of 
accounting. The liability or indebtedness for expenses is in- 
curred previous to receipt of income in practically every case. 

24. The Total Investment. — The total capital invested in 
a business is always greater than that represented by the cost 
of the assets listed under the capital account. Were income and 
the items charged under expense to occur simultaneously, the 
one should cancel the other, leaving the surplus or profit to 
apply as interest or dividends on the capital originally invested. 
After a business is established, this actually takes place and unless 
the scope of operations is enlarged, the capital required should 
not subsequently increase. But this apparent coincidence of 
income and outlay does not alter the time relation shown to 
exist between them. The expenditures of to-day are for the pur- 
pose of securing future income, while the income of to-day is the 
result of past outlays. 



OUTLAY AND INCOME 1 5 

These outlays, whether in form of services or purchases, must 
be paid for by the proprietor at the time they are incurred, 
either in money or credit. This evidently requires an addition 
to the total capital invested, sufficient to meet all expenses 
covering the period of installation or formation of the business, 
or the time elapsing between outlay and income. If the income 
is regular and continuous, this required capital ceases to increase 
as soon as current income exceeds current outlay. But the sum 
invested up to this point remains in the business, for whatever 
portion may be paid back out of income an equal sum is at 
once required to meet the expenses for which the corresponding 
future income has not yet materialized. 

The capital required to meet these current expenses and carry 
them continuously, thus bridging the gap between outlay and 
income, is termed working or floating capital, in contrast to 
that represented by more durable assets shown in the capital 
account. 

For business in which income is realized only at long intervals, 
expenses continue during the period, and the amount of working 
capital tied up in wages and suppHes increases rapidly to large 
proportions, and is as suddenly decreased when the income is 
received. Such a condition is represented by the business 
of driving logs down streams. Contractors engaged in this 
work receive their settlement when the logs reach their desti- 
nation, which is once a year, while frequently a drive is hung 
up and lays over a season. It was formerly the custom in some 
states to transfer this indebtedness or outlay to the shoulders 
of the laborers, who were paid in time checks made payable 
in cash at a date subsequent to the probable delivery of the 
drive. The men, being without capital, cashed these checks 
at discounts which allowed the bankers or speculators who 
furnished the funds to make very large profits. These profits 
were in some cases split with the contractor who issued the checks. 
Legislation has in most instances required cash payment of 
wages, thus requiring the contractor to assume this obligation 
and raise the necessary working capital. Where, as in the case 
of forest plantations, the period elapsing between outlay and 



1 6 FOREST VALUATION 

income becomes abnormally long, the amount of capital required 
to carry the project to completion is proportionally increased. 

25. Cost Accounts. — A cost account differs from a general 
profit and loss account in that it analyzes the cost of producing 
a given unit of output, instead of accounting for the current 
outlay and income of the business as a whole. Such an account 
traces the history of the product from the time of its purchase 
or inception until it is sold. The costs incurred fall into two 
groups: specific costs, which include that for raw materials 
and labor directly applied in production; and overhead charges, 
which include taxes, insurance, light, fuel, superintendence, 
rent and other items, which must be apportioned on an equitable 
basis over the entire output. Cost accounts in forest production 
sum up the cost of growing a crop of timber from origin to matu- 
rity. Owing to the great length of the period involved, the 
factor of compound interest on invested funds, when introduced 
as a cost in such accounts, becomes one of the largest items of 
expense. 

26. Income. — In § 8 and § 9 it appears that prices for fin- 
ished products are the source of value for all forms of property. 
Value, as distinguished from cost, depends upon net income and 
looks to the future. The income from finished products, which 
gives them their value, corresponds with the services they are 
capable of rendering by being used or consumed. 

The sources of income from productive property consist 
either of finished products or materials in a raw or unfinished 
state, while the income derived from the business of operating 
such properties is the money received from the sale of the output. 

27. The Economic Opportunity. — To derive or produce 
an income, some human want must be supplied. The greater 
the range and diversity of these wants and the greater the 
purchasing power or capacity of the average individual to 
gratify them, the more numerous and promising will be the 
economic opportunities for business. Inequalities in the dis- 
tribution of wealth, and the existence of a pauper class, greatly 
diminish the total business of a nation and divert much of it 
into wasteful and injurious channels. 



OUTLAY AND INCOME 17 

28. The Business Venture. — Income can be produced only 
by risking capital and expending elTort on the chance that this 
outlay will be returned " with interest." In a properly con- 
ducted business this risk is assumed by the proprietor, who 
makes himself personally responsible for the management. 
Ownership is represented in modern business by capital stock. 
By means of this same device, extensive frauds are possible by 
which the real managers of a business shift both risk and loss 
to the stockholders or owners. Legitimate risk, borne by those 
responsible for the results, is unavoidable and is one of the 
chief characteristics of the business venture. Aside from the 
risk of accidental losses by fire, theft and other factors, the final 
ever-present risk is that income will be insufficient to offset the 
required outlay, and insolvency result. 

29. Exchange. — Income from business (§ 26) is derived 
almost entirely from sales of merchandise or manufactured 
products, which constitute an exchange of goods for money. 
The transaction is in theory completed with the delivery of the 
goods, but payment is often deferred and constitutes a debt 
on the part of the purchaser, which is a debit or asset to the 
business. The losses which occur through ultimate failure of 
debtors to pay are finally debited as an expense. 

30. Disposition of Income. — With the receipt of income 
the cycle of effort is completed and the purposes of the business 
are accomphshed. An accounting must now be rendered to 
the owner. In case the proprietor's account and ownership is 
terminated by a sale of the entire business, the settlement would 
consist of: 

Payment of outstanding bills, wages and other outside obli- 
gations. 
Return of outstanding and borrowed capital. 
Distribution of surplus as profit to owners of the capital 

invested. 
In the annual accounting of a going concern the profit and 
loss account takes care of the expenses. The surplus or deficit 
in annual income, shown as profit or loss, is carried into the 
annual balance sheet for future disposal. 



l8 FOREST VALUATION 

31. Returns on Capital. — Out of the net profits after can- 
celling the expenses for the year, provision must first be made for 
the replacement of capital assets lost by depreciation or other- 
wise. The remainder is available as returns on capital. 

Here a sharp distinction must be made between the total 
amount of capital required to finance a venture and the persons 
or sources from which this capital is derived. From the stand- 
point of the business itself, the source or ownership of this 
capital has no effect upon the total net profits but affects merely 
the apportioning of these profits. 

A proprietor who furnishes his entire capital, both fixed and 
working, takes all the profits and assumes the risk of loss. But 
it is an almost universal custom to borrow part of the needed 
capital on the security of the business or of the fixed assets. 
In this case profits are earned on the total invested capital as 
before, but the division is on a different basis. The borrowed 
capital receives a fixed rate, agreed upon at the time of secur- 
ing the loan, and guaranteed by the proprietor. He receives 
in turn the entire surplus remaining after this obligation is 
met. 

32. Interest versus Dividends. — The sum guaranteed to 
the lender of borrowed capital is interest. This is paid out of 
net income and is as much a part of the net earnings of the busi- 
ness as the remainder. The residue is either left in the business 
as additional capital, or paid to the proprietors as dividends. 

Interest, at the rate demanded on borrowed funds, will require 
a given sum on the entire capital. Should the business earn a 
net income exceeding this sum, the proprietor receives the excess, 
which raises the rate earned by his own capital, or his dividends, 
above the rate of interest paid to creditors. The greater the 
proportion of capital he borrows, the greater will be the rate of 
dividends on the lessened capital of the proprietor. But on 
failure of the business to earn the rate paid on borrowed funds, 
the owner bears the entire loss, and the smaller the proportion 
which his capital bears to the whole investment, the greater is 
his relative loss. 

In an insolvent concern, the owner's capital, as well as divi- 



OUTLAY AND INCOME 1 9 

dends, is sacrificed before any loss of either interest or capital 
is permitted to fall upon the holder of mortgages or liens. For 
this reason bankrupts may fraudulently conceal the assets and 
thus defraud creditors. 

33. Profits. — According to Marshall,* " When a man is 
engaged in business his profits for the year are the excess of his 
receipts from his business during the year over his outlay for 
his business. The difference between the value of his stock 
and plant at the end and at the beginning of the year is taken 
as part of his receipts, or as part of his outlay, according as 
there has been an increase or decrease of value. What remains 
of his profits after deducting interest on his capital at the current 
rate may be called his earnings of undertaking or management." 
According to this definition, interest paid on borrowed money 
is excluded from profits, but interest on the owner's capital is 
considered as constituting part of the profits. This is the dis- 
tinguishing point between a purely economic or impersonal 
consideration of a business and a personal account with the 
proprietor. In an economic consideration of the general, ques- 
tion of profits on an industry as a whole, such as is needed, for 
instance, in the process of appraising stumpage values for stand- 
ing timber (Chapter XI) , the distribution of the required capital 
between proprietors and creditors has no significance. The 
entire net revenue available as returns on capital for the current 
year must be regarded as profits. 

34. Wages versus Profits. — Wages are an outlay, or an 
expense, which serves to diminish profits. The wage or salary, 
ultimately met from income, is the share of the wage earner 
in the returns of the enterprise. 

In most undertakings the owners themselves give at least 
part of their time to the management of the business. In very 
small enterprises the owner may even do most of his own work, 
thus saving the expense of employing labor. The larger forms 
of business, in which the ownership is scattered in the form of 
capital stock, are managed by proxy, through boards of direc-. 

* " Principles of Economics," by Alfred Marshall, 5th Ed., Vol. I, p. 142. 
Macmillan & Co., London, 1907. 



20 FOREST VALUATION 

tors who devote but a small portion of their time to these duties. 
There is an almost complete separation between wages or salaries, 
and income in the form of dividends. Even in such cases, 
capable managers are frequently given an interest in the business 
and their returns thus include both wages and dividends, although 
the two items are separately accounted for. In small ventures 
managed by the owner, this distinction is often neglected, and 
the owner's profits are the sole source of compensation for his 
time. In such cases a sum representing the wages of the manager 
or overseer should be charged to expense. Should the business 
pay less than this sum it is unprofitable. 



CHAPTER III 
INTEREST 

35. The Problem of Interest. — In proprietary accounts, 
all items, with the exception of interest, are easily classified as 
costs or as income. Interest may be regarded as either cost 
or income, according to the point of view. Since these two 
conceptions are not interchangeable, a clear understanding of 
this problem is necessary to avoid errors in dealing with ques- 
tions of valuation accounting. 

36. Interest as a Cost. — Interest when regarded as a cost 
must be considered in its relation, first to the owners of capital, 
and second, to the capital itself. In accounting, the interest 
paid upon borrowed capital is regarded by the proprietors as a 
cost. But it must be noted that the net profits of the business 
are first computed, and from these profits, rather than from 
gross income, the cost of interest is met (§32). This item of 
cost is entirely a personal matter between the owner and his 
creditors. Should there be no borrowed capital, this cost item 
would disappear from the account, and dividends or additions 
to surplus, to an equal amount, would be substituted. 

But since borrowed capital is entitled to receive interest at a 
standard rate, and this "cost" must be met, the owner con- 
siders that his own capital is entitled to receive interest at a 
like rate. He guarantees payment on loans, but must depend 
on his own exertions to obtain this interest on both the borrowed 
funds and on his own investment. Should he prefer the role of 
money lender, his capital will earn this rate of interest without 
the risks attendant on the business venture. The risks of lending 
money upon good security are much less than those accom- 
panying other forms of business. Shall he therefore charge 
interest upon his entire capital as a cost which must be met? 
Those who take this view will include interest, not only on 



22 FOREST VALUATION 

borrowed funds but on the total invested capital, in the same 
category as other expenses, that is, as a part of the so-called 
carrying charges of the business. 

The interest to which the owner is entitled cannot be entered 
in proprietary accounts as an actual charge or cost similar to 
interest on borrowed funds. His share of interest is never 
actually expended, and the idea of cost exists merely by impli- 
cation. But in a cost account, which is intended to present 
definitely the relation between total cost of production and 
resulting income, interest may be calculated and entered as a 
part of the total cost. 

37. Interest as Income. — Whether or not interest is re- 
garded as a cost, it always represents income on the capital 
investment, and in this respect differs from other costs. All 
other items of expense, such as taxes, wages and cost of supplies, 
while met eventually from income, go to persons or enterprises 
other than the capitalists who finance the venture. And just 
as the creditors of the business, during the formative period, 
are paid in advance by the capitalist, who receives returns 
finally from income, so the capitalist who only loans money and 
does not assume the risks of ownership may receive his interest 
in advance of income, provided it falls due and is paid by the 
proprietor. But this cost to the latter is ultimately returned to 
him from income, which must also pay him returns on his own 
investment. In case the income is continuous and is accounted 
for annually, both borrowed and invested capital receive income 
directly from the net returns. 

38. The "Rate of Interest." — Interest has been defined as 
the price of time differences in the enjoyment of income (§ 14). 
Since the use or borrowing of capital is the means of anticipating 
income (§12), and the value of both capital and interest is ex- 
pressed in money, it follows that interest is the price of the use 
of money. 

This price for money loans is termed the "rate of interest." 
As money is more desirable than other forms of capital because 
of its universal acceptability as a medium of exchange, and as the 
risk in money lending is normally less (§ 36) than in business. 



INTEREST 23 

this rate of interest, which represents the possible income on 
capital in the form of money, becomes the standard by which 
the desirability of any other form of investment is gauged. 

39. The Profits of the Undertaking. — Unless there is a 
chance of earning a larger rate of income upon the capital re- 
quired in an undertaking than could be earned by lending this 
capital to others, there would be no incentive to assume the 
risks of the business. In order to make a business really profit- 
able, the net income should exceed this ''rate of interest." 
This surplus is the goal of the whole operation and is termed the 
"profits of the undertaking," as distinct from the term "profits," 
which includes interest (§ 33). It is the personal reward of the 
individual who has borne the responsibility of the business. 
There is no good English word to indicate this person. Un- 
fortunately we have appropriated the word "undertaker" for 
other uses. The French term "entrepreneur" is commonly 
accepted by economists. The more recent English substitute 
"enterpriser " is rather clumsy, but will be used in this text. 

The term "profits of the undertaking" would therefore ex- 
clude interest as a necessary "cost" and regard the margin 
remaining as the real profit. 

40. Annual Profits. — On this basis, a business paying annual 
dividends is considered successful if the average dividends are 
larger than the rate of interest which the firm has to pay on 
borrowed capital. If the dividends are less than this, the busi- 
ness is considered unprofitable to the owner, although it may be 
relatively more profitable to continue it than to abandon or sell 
it, with resultant loss or impairment of capital. As a matter of 
fact, only the more capable and experienced managers succeed 
in earning an "enterpriser's profit," and one per cent of independ- 
ent concerns annually become insolvent, thus failing to earn a 
net income sufficient even to protect the capital investment.* 

41. Deferred Profits. — In an enterprise in which outlay 
precedes income by an interval greater than one year, the method 
of accounting for profits depends upon whether this condition 

* The Percentage of Failures, Dun's Review, May 31, 1913. R. S. Dun & Co., 
New York. 



24 FOREST VALUATION 

of affairs is normal or accidental, expected or unforeseen. If 
profits should normally be earned annually, failure to do so in 
any given year would be regarded as a loss by the proprietor, 
but this would be mentally "written off" against the current 
year and not carried as a debit to be recovered from the income 
of a subsequent year. 

If the enterprise is planned to extend several years before 
realizing profits, as in the case of the voyages of whaling ships, 
or the production of timber from plantations, the annual interest 
which remains unpaid is not considered lost, since it is the expec- 
tation of the owners that this will be more than made up when 
the "ship comes in." But the profits of the undertaking may 
still be computed separately from the standard interest "cost" 
or income. This must be done by calculating compound interest 
on all cash expenses as long as they remain unpaid, which gives 
the sum that could be earned by the capital as loans in money 
form for an equal period. 

The deferred income may greatly exceed the total cash outlay 
and the enterprise yet fail to earn compound interest at a 
standard rate. In this case the deferred "profits of the under- 
taking" disappear, and the status of the venture is the same 
as that of the business whose annual dividends fall below the 
standard rate of interest. 

The production of timber as a business is based largely on 
the theory of deferred profits, and both the determination of 
these profits and the methods of accounting employed should 
be made to conform to the essential differences between such a 
business and one conducted on the basis of annual profits. 

42. Income versus Profits. — In determining the amount or 
rate of profit which should be earned in order to properly com- 
pensate the enterpriser, the status of interest must be held 
clearly in mind. It is a "cost" merely for purposes of sepa- 
rating that portion of the income which his capital could earn 
from the additional income earned by his personal efforts. In 
impersonal consideration of the legitimate profits of a business, 
the distinction between borrowed capital and proprietary capital 
is rejected, and the interest upon the entire capitalization is 



INTEREST 25 

included in the income earned and not in costs. Should the 
fallacy be introduced of considering interest as a cost in comput- 
ing profits, the apparent profit required would be increased 
abnormally. For instance, it is stated that a certain business 
should earn a profit of 10 per cent, which, with interest at 6 per 
cent, indicates an enterpriser's profit of 4 per cent. By consid- 
ering this interest as an actual cost, an additional profit of 10 
per cent might be expected. But, in reality, this 10 per cent 
would be the enterpriser's profit. The total net income must 
then be 16 per cent, and the enterpriser's gain is 2^ times as 
great as in the original case. If an enterpriser's profit of 10 
per cent is necessary, the "profits" of the business must be 16 
per cent and not 10 per cent. 

The larger the amount of capital invested in a business, the 
smaller, as a rule, will be this margin between income and 
interest, which represents the enterpriser's gain. Both income 
and "gain," while larger in amount, average less in proportion 
than on small investments. This shrinkage does not come 
entirely on the margin of gain, since funds can probably be 
borrowed at lower rates in such undertakings. The longer the 
time elapsing before income is received, the less will be this 
margin of profit over compound interest at standard rates. 
For very long investments, the enterpriser's gain tends to dis- 
appear, and is entirely dependent on the rate of interest chosen 
as representing the legitimate income on the capital itself. 

In both the above cases, in spite of the shrinking of enter- 
priser's profits, the income or profit over expenses remains in 
the form of interest returns, and, especially on long time in- 
vestments, the final results may still be considered by the inves- 
tor as highly satisfactory. 

This attitude is partly due to ignorance. The owner of un- 
productive property, such as unimproved real estate, seldom 
keeps a cost account which shows him the total outlay repre- 
sented by the purchase price plus taxes and improvements, and 
still more rarely does he add the "cost" of the unearned interest 
on this total from year to year. When he sells this property 
after the lapse of several years, for more than double what he 



26 FOREST VALUATION 

paid for it, he does not realize that a savings bank at 4 per cent 
might have paid him more for the uninterrupted use of the same 
capital than his profit amounts to. 

Yet this attitude of investors towards deferred profits is not 
explained wholly by ignorance. If an investor is in a position to 
get along without income for a long period, at the end of that 
time the "loss" of annual income has but little significance 
and he sees only the accumulated total of his profit. He com- 
pares this with his original outlay and judges results on that 
basis. This tends to make him satisfied with a return which in 
reality represents low rates of interest on such investments. 

43. Influences Determining the "Rate of Interest." — The 
current rate of interest is a price, determined by the demand 
and supply of money for borrowing purposes. This price or 
rate has no greater stability than the average prices of other 
commodities. It fluctuates during the year, and over longer 
periods, in response to changing economic conditions. Nor is 
this rate the same for all classes of loans. It varies with the 
security offered, the length of the period covered by the loan, 
and the personaHty of the individuals negotiating it. In spite 
of these variations, an average rate of interest may be roughly 
approximated for a given time and place; but this is determined 
far more closely if the circumstances affecting the particular 
loan are also known. 

44. The Influence of Personality on the Rate of Interest. — 
Just as prices are the resultant of human opinions interpreting 
desires or demand and weighing them against efforts or supply, 
so the rate of interest depends even more completely upon the 
human character and mind. 

Impatience for income, and preference for present over future 
income, tends to raise the price the individual will pay for this 
privilege. Persons who lack foresight, are improvident and 
are lacking in self-control will borrow at high rates. The same 
is true of persons who lack capital and are in need of present 
income. On the other hand, individuals who desire to provide 
for the future, who possess the power of self-denial and who are 
already possessed of considerable capital will borrow, if at all, 



INTEREST 27 

only at reasonable rates. As investors, the former group desire 
to "get rich quick" and by seeking abnormal profits usually 
lose what capital they may possess. The latter group are apt 
to favor long time investments which give a certain return even 
at a low rate. 

45. Risk and Expense. — As most loans of money are made 
on the basis of a security pledged as a guarantee for repayment, 
and worth more than the amount of the loan, the risk of loss 
of principal or interest is correspondingly reduced. In case of 
unreliable parties, notes are guaranteed by some one who is 
able to pay. Risky loans are made at higher rates than safe 
loans, the extra rate being intended to cover average losses. 
The exorbitant rates charged by loan sharks are not justified on 
this basis, although loans of this character require a somewhat 
higher rate than business loans. Such rates are due to personal 
elements, exaggerated by defective laws and bad economic con- 
ditions, which permit the exploitation of a class of persons unable 
to protect themselves. 

Expense of placing loans and of collecting interest tend to 
increase the rate of interest charged. This expense is greater for 
short loans, and the funds are apt to be idle part of the time. 

It follows that the lowest rates of interest are received on 
absolutely safe securities, which run for a long period and upon 
which the interest payments are made without expense to the 
owner. Government securities and bonds of high grade fulfil 
these conditions. 

46. Fluctuating Value of Money. — Should money fall in 
value or in purchasing power, the rate of interest tends to rise 
to a degree corresponding to the average annual loss in the value 
of the capital. Only by this means can a lender of capital escape 
actual loss. If the fall in value amounts to i per cent per year, 
securities upon which the normal rate of interest is 4 per cent 
will be worth in purchasing power only 99 per cent of their 
original value at the close of the year. A rate of 5 per cent 
enables the investor to replace this difference by adding it to the 
capital. 

Such losses usually escape the notice of the owner, who imag- 



28 FOREST VALUATION 

ines himself as wealthy as before even if he spends the entire 
income from his investment. 

47. The Rate of Interest for Business Investments. — The 
rate of interest for a business is the rate at which money will 
seek investment in the enterprise. It is a question whether 
or not this basic rate should include an enterpriser's profit. 
The rate which the lender of capital will accept on the security 
of the business, or what the proprietor can obtain as the basis 
for a loan, is a conception tallying rather more closely with actual 
conditions. Such a rate may be said to attract capital, but it 
may not attract the enterpriser, who hopes to do better. The 
"rate" adopted as the standard for an investment becomes 
the basis for computing both the cost of production (§25) and 
the value of the assets (Chapter IV). 

48. The Effect of Deferred Income upon the Rate of Interest. 

— A mathematical comparison of simple and compound interest 
leads to the conclusion that, since the latter, as applied to de- 
ferred returns, is the exact equivalent of the former when returns 
are annual, a given basic rate should be the same whether the 
investment pays annual or deferred income. 

But under the definition that the "rate of interest" means 
the rate which will attract money to a business, the above 
conclusion must be tested by the "price making" factors 
which influence the minds of investors. Should these factors 
be found to differ for investments of the two classes, the basic 
rate of interest applicable to each case will differ to a corre- 
sponding degree. 

49. Comparison of Results of Simple and Compound Interest. 

— The economic results obtained in actual practice from an 
undertaking which produces simple or annual interest are not 
the same as those obtained by compound interest, however 
similar may be their mathematical relation. 

To make the returns from a business which starts with a 
definite amount of capital, and earns annual net profits at x 
per cent, equal to those from the investment of a similar sum 
which will produce compound interest after a term of years at 
the same rate, x per cent, requires several assumptions. The 



INTEREST 29 

entire earnings of the business would have to be retained as 
capital and not a cent withdrawn as dividends. This capital 
must then be utilized in such a manner that it will produce net 
earnings equal in rate to the earnings on the original capital. 
Each year this process must be repeated, resulting in an expan- 
sion of the business at a geometric rate. If this result is ob- 
tained, the total capital at the end of the period will not be 
worth one cent more than the funds accumulated in the second 
investment, where all income is deferred until the end of the 
period. 

Should the proprietor withdraw any portion of the earnings 
during the entire period, or should the business fail to expand 
annually at the required per cent, the resultant rate of com- 
pound interest earned by annual profits will be lowered below 
that demanded in the comparison. 

50. Limitation of Opportunity. — Such compound expansion 
of a business is possible only where the economic opportunity 
(§ 27) is practically unlimited, or increases at a rate which keeps 
pace with the growth of the business. This occurs only as a 
temporary condition, both in business and in all other forms of 
activity. 

Animal and plant life have the capacity for expansion at geo- 
metric ratios comparable to enormous rates of compound in- 
terest; such events seldom occur, but when they do, the result 
is calamitous. English sparrows imported into America found 
an environment not used by any existing species of bird. Until 
this niche had been completely occupied, the sparrow increased 
at a compound rate. The species is now merely holding its own. 

In manufacturing, the production of new articles and the 
growth of a demand for them, as in the case of automobiles, 
creates an opportunity which permits of a trade expansion at 
geometric or compound rates for a while. This expansion took 
place when bicycles were first made popular. It cannot con- 
tinue in_any line at the same rate over an extended period. A 
lessening, not of the annual demand, but merely of its rate 
of increase, has the effect of preventing further expansion at a 
like rate, and with the establishment of equilibrium, not only 



30 



FOREST VALUATION 



will compound interest fall to a lower rate, but annual profits 
will be reduced as well. This explains the fact, accepted by 
economists, that the larger the aggregation of capital employed 
in an undertaking, the smaller will be the annual rate of profits 
which justifies the investment. 

The conclusion is irresistible, that the mathematical equality 
between simple and compound returns does not hold good. 
The latter tends to fall below the former, and, what is more 
important, this discrepancy is accepted as equitable by investors. 
The recognition of this fact will go far towards clearing up 
the false impressions which at present obscure the question of 
rates of interest applicable to forest investments. 

51. Effect of the Rate of Interest upon Accumulations of 
Compound Interest. — The cumulative effect of compound 
interest bears an intimate relation to the rate of interest. Low 
rates cause a very slow increase and may be applied with some 
reason to investments which run for a very long period. High 
rates cause a very rapid increase which soon passes the bounds of 
possible attainment in practice. The following diagram reveals 
this relation. (See Diagram I.) 

TABLE I 

Comparison of the Results of Simple and Compound Interest 
ON $ioo AT THE End of a Period of 50 Years 







Rate of simple in- 


Rate of 


Value of capital 


terest to be earned 


interest 


and interest at 


and saved to 


earned 


end of period 


give equal final 
results 


Per Cent 




Per Cent 


I 


$164 


1.28 


2 


269 


3-38 


3 


438 


6.76 


4 


710 


12.20 


5 


1,146 


20.92 


6 


1,842 


34-84 


7 


2,946 


56.92 


8 


4,690 


91.80 


10 


11.739 


232.78 



A comparison of the economic results of simple and compound 
interest is further brought out by the above table which gives 



INTEREST 



31 



DIAGRAM I 

Periods Reqihred for $1.00 to Multiply, at Different Rates of 
CoMPOtTND Interest* 



20 
19 
18 
17 
16 
15 
-14 

03' 

1l3 

•a 

■312 

.S 

•all 


010 

(B 

h 
















10-* 


s-:" 


7f« 




6fo 




S-^t 


















/ 


1 








I 


















/ 






/ 


/ 






1 
























/ 






/ 












1 




/ 








/ 






/ 
















/ 


/ 






/ 




1 


/ 














/ 


/ 




1 


] 


' 




















/ 


/ 


/ 




/ 






1 














/ 


/ 


/ 


/ 




/ 




















/ 


/ 


/ 


/ 


1 


' 




/ 


















' / 


y 


/ 






/ 


1 














/ 




/ 


/ 


1 


1 




/ 






/ 










/ 




/ 


/ 


/ 




/ 


f 






/ 










/ 


/ / 


\/ 


t 


/ 




/ 






/ 






6 
5 

3 
2 
1 








/ 


/ 


/i 


J 


/ 




/ 






A 


/ 










/ 


/ 


V 


/ 


/ 


/ 


/ 
















J 


// 


/ 


/ 


/ 


,/ 


/ 


y 


y 














/ 


^ 


y^ 


/ 


y 


^^ 


^ 


^ 








-^ 






/ 


^ 


y> 


y 


^ 




U 


^ 




'^ 










r^ 


m 




s=^ 


— 












' 









































4«5 



25S 



Vf. 



30 



40 
Years 



50 



GO 



70 75 



* A rate of 10 per cent, compounded, multiplies 20 times in 31 years. A rate of 
I per cent compounded, doubles in 70 years. Even 6 per cent would, in 70 years, 
multiply the principal 59 times. 



32 FOREST VALUATION 

the total amount to which the sum of $ioo will increase in 50 
years, provided the investor complies with the conditions out- 
lined in Article 49. 

The final column shows the rate which the original invest- 
ment would have to earn annually to get the same results, pro- 
vided the entire income were placed in a deposit vault and 
saved until the end of the period without reinvestment. Should 
the proprietor spend the annual income, he would have merely 
the original capital of $100 left at 50 years. 

52. The Rate of Interest in Forest Investments. — To de- 
termine the basic rate of interest applicable to investments 
in forestry, two factors must be analysed, namely, the relative 
security of the investment, and the financial nature of the enter- 
prise. It is claimed by advocates of a high rate on forest invest- 
ments that this is justified by the ever-present risks from fire and 
other destructive agencies, and also by the length of the period 
elapsing between outlay and income, which makes the invest- 
ment less desirable unless it can be shown to be more profitable. 

The first of these claims must be admitted. Risk should be 
provided against by demanding higher interest. This subject 
is discussed in Chapter XIII. Risks must be judged on the 
basis of comparison with those assumed in other lines of in- 
vestment, and due weight must be given to the present 
development of measures of protection on the part of states 
and associations. 

The second claim is fallacious. To demand a higher rate of 
interest the longer the returns are deferred is a subversion of the 
economic laws applicable to all forms of investment. The desir- 
abihty of the investment as affected by the difference between 
annual and deferred returns will not modify the rate of interest 
which should apply, but rather, will determine the class of 
persons who are apt to choose such an investment. And since 
those persons who are the most apt to favor long-term invest- 
ments with deferred income are those possessed of foresight, 
making provision for their children, and with sufficient capital 
for their personal needs (§ 44) , such persons will accept a lower 
rather than a higher rate of interest, and in many cases will not 



INTEREST 33 

even compute the probable rate, being content with the general 
prospect of a future value greatly in excess of present investment. 

53. Comparison of Interest Rates in Forestry with Other 
Investments. — Proper rates for forest investments can only be 
judged on the basis of comparison with other forms of enterprise. 
If the scope of the comparison is confined to forest production 
and the account covers the period requisite for growth, a com- 
parison between forestry and business producing annual income 
is impossible. The goal of forest management is the forest 
which wlU yield annual returns, but each crop represents the 
accumulated outlay throughout its Hfe and must be so judged 
in comparing interest rates. 

The only enterprises familiar to the pubUc, which are reckoned 
on a basis of compound interest, are savings banks and Hfe 
insurance companies. The former have paid an average of 
3 per cent, but of late years 4 per cent is common. Most banks 
do not permit the accimiulation of compound interest on accounts 
to run more than 20 years without some sign of active interest 
on the part of the owner, manifested either by withdrawals or 
additional deposits. If the owner is alive and can refrain from 
depleting his account for fifty years and the bank remains 
solvent, he can obtain compound interest for that period. Such 
cases practically never occur. 

The average period covered by the risk of a life insurance policy 
is not over 13 § years,* and most companies calculate that they 
can earn compound interest at about 4 per cent on the money 
invested in policies for this average period. 

For periods longer than fifty years there is no basis for com- 
parison by which the rates reasonably applicable to forest 
investments can be judged. Based upon the economic laws 
outlined in Articles 47 to 50, it must follow that those rates 
will be less than 4 per cent provided the investment offers equal 
security with life insurance and savings banks. Should the 
security be considered less safe, the increased rate demanded 
would offset the reduction in rate called for by the length of 
the period of investment, and the investment should not require 

* The Brown Book of Life Insurance Economics. Edition of 1911-12, p. 13. 



34 



FOREST VALUATION 



a rate appreciably higher than 4 per cent for periods of over 
50 years. 

If these arguments are admitted, it is possible to show that 
the income which may actually be earned by forest investments 
covering long periods will be equivalent to the rates demanded 
by the character of the investment, even though the earnings 
may fall as low as 3 per cent for periods of over 50 years, and 
2I per cent to 2 per cent for periods exceeding 100 years. 



CHAPTER IV 
VALUATION OF ASSETS 

54. Valuation Accounts. — A valuation account is a specific 
statement (§ 19) of the value of assets, whether material or con- 
sisting of intangible rights. It informs the owner of the present 
condition of the property, and enables him to compare this con- 
dition and value with the total net cost or investment (§22), and 
thus determine whether the business as a whole is gaining or 
losing (§28). To accomplish this purpose, the account should 
show what the business or property is actually worth at the 
present moment, not merely what it was worth when the assets 
were first acquired. 

55. The Inventory. — In order to determine value we must 
know the quantity of goods on hand and what each imit is worth. 
This process of taking stock is termed an inventory. It is not 
complete with the mere Usting of goods, but includes their valu- 
ation. In forest management the process of estimating standing 
timber and other forest resources, often termed reconnaisance, 
is the means of obtaining this data. 

56. Cost as a Basis of Value. — Conservative accounting 
seeks to avoid inflation of the value of assets, with its corre- 
sponding indication of false profits in the balance sheet. If an 
asset has been purchased in good faith, the purchase price is 
taken to represent its true value. All items of investment 
representing assets of such a character that they would be 
included in the capital account will be accepted at cost, less 
depreciation, in the valuation of assets. This does not mean 
that the cost of an article represents its present value, but merely 
that cost is definitely known and, when corrected for deprecia- 
tion, is accepted as a conservative basis for value. 

57. Expenses and Interest versus Value. — While account- 
ants approve of the acceptance of capital expenditures or original 

35 



36 FOREST VALUATION 

cost of purchase of tangible assets as a basis of value, they 
condemn the assumption that subsequent expenses, or items 
customarily entered under outlay and income, or profit and loss, 
add anything to the value of assets or furnish a basis for valuing 
these assets. The theory is that such expenditures are made 
for the direct purpose of producing income sufficient to offset 
them, and that if this result is not secured, the loss must be shown 
as a deficit, and not concealed by adding an equivalent of this 
loss to the value of the assets. 

This theory is justified for business undertakings supposed to 
produce annual income, for if the income which should cancel 
expenses fails to do so, the deficit cannot be construed to 
represent anything but absolute loss, leading to insolvency. 

This reasoning is then extended to apply to undertakings 
in their formative period (§ 23), and the practice of retaining 
investments in the inventory at their original cost is highly 
commended, in spite of the fact that practically all expenses 
during this period require additions to capital (§24), and this 
treatment of assets is thus bound to result in an apparent deficit 
or state of insolvency. 

Yet no one would undertake such long time investments 
unless he expects an increase in the value of his assets in a meas- 
ure corresponding to or paralleling the accumulation of cost 
and interest. That this fact is assumed has a remarkable con- 
firmation in the revolutionary practice of accounting authorized 
in case of railroad properties during the course of construction 
and before it is possible to earn an income. In Germany and 
England it is permitted by law to include as an addition to the 
value of the assets, not only the revenue expenditures during 
construction, but the interest on bonds and dividends to stock- 
holders.* This is the very process so vigorously and justly 
condemned in case of business undertakings which should pay 
annual dividends, nor would it be tolerated in the case of rail- 
roads except during the period of construction. 

A case closely parallel to the above is found in forest planta- 

* "Modem Accounting," by Henry Rand Hatfield, pp. 76, 77. D. Appleton 
& Co., 1909. 



VALUATION OF ASSETS 37 

tions. Shall the value of such property be based on the 
purchase price, plus expenses, plus unpaid or deferred interest, 
representing the total "cost" or "cost value" of the property? 
As in the case of the railroad this might be justified. But such 
"cost" is only an indication of value in either of these instances. 
Unless the property is of such a character and its promise of 
future income is such that this increase in value is sure to occur 
and is evidently taking place, no one would be deceived into 
thinking that such a cost calculation corresponded in the least 
with value. Even then the value might be more, or less, and 
there is no reason for assuming that it is accurately gauged by 
cost. 

58. Essential Difference between Cost and Value. — The 
reader must keep clearly in mind that the valuation of assets is 
a process essentially different from the account of cost and ex- 
penses (Chapter I, Articles 2 to 11 inclusive). If costs are taken 
as the basis of value, as is done in some instances (§56), they 
are merely the source of the information used, but this informa- 
tion might as readily be obtained from entirely different sources, 
and frequently must be so acquired. Value is determined for 
the purpose of comparison with costs to indicate profit or loss. 
If it were identical with cost, no comparison would be possible 
and the owner could not determine his probable profits. 

59. Sale Value as a Basis of Value. — In case a business 
changes hands by sale, the sale value so determined is accepted 
as the value of the business. In this transaction the price paid 
for the assets must be entered as their value on the books. 
Such sales thus establish a new recorded or book value for these 
assets. The fact of the sale is the most convincing evidence of 
value, although even this is not final proof, for one or the other 
of the parties may have been deceived or handicapped in the 
transaction. Nor will a past sale be accepted as absolutely 
determining a future sale value even for the same property; 
in fact it is usually the reason for desiring a different value. 
Sales of property or business have a profound effect upon pro- 
prietary accounts, in that the former owner receives at once all 
his income and capital and can balance his books and determine 



38 FOREST VALUATION 

his total net profit, while the purchaser is saddled with a cost or 
investment which forms the opening entry in a similar account, 
and no future acts will serve to reduce this initial cost. 

60. Appraisal of Value (§ i8). — In determining the true value 
of assets, either as a guide to the owners in negotiating a sale, 
or for compensation for damages or in condemnation pro- 
ceedings, the appraiser bases his opinion upon the most reliable 
sources of information at hand. If a basis for sales is sought, 
the average sale value of similar property in the immediate 
past is given most weight. But where the owner does not 
desire to sell, the appraiser must seek to establish the value 
to the owner if the property remains in his possession, and this 
rests wholly on its usefulness to him, not on what someone else 
would pay for it. 

61. Future Income as the Basis of Value. — The only true 
basis of value recognized by economists is income (§§4, 26). 
When a sale of property occurs, the ''income" from the sale 
should coincide with the value of the property. The value 
which the owner or purchaser places on the property is deter- 
mined by the value of all the future income which he expects to 
derive from it. 

In explaining values on this basis the true nature of income 
must be kept in mind. "Final" income takes the form of 
actual enjoyment of the uses or services of possessions. Real 
estate is valuable to an owner, not merely for its money income, 
but for the personal enjoyment which he gets from the rights 
of possession. In this must be included the associations and 
neighborhood of which it makes him a part. The sentiment 
attached to the retention of an inherited homestead, the prej- 
udice against leaving surroundings grown familiar by long resi- 
dence will, by contributing to the peace of mind of the owner, 
enhance the value of his land in his opinion in a manner fully 
as concrete as money income. Only poverty or actual want 
will counterbalance these very real values. This element of 
social income must never be lost sight of in the valuation of 
property. But the appraisal of income must ordinarily be based 
upon money returns which can reasonably be expected in the 



VALUATION OF ASSETS 39 

future, and the present value of the property rests upon the 
mathematical relation between the future income and its dis- 
counted value. 

62. Capital Value or Expectation Value. — Capital value, or 
expectation value, is the net value of property based upon future 
income. It is the capitalized value of future income minus 
future expenses. The terms "capitalized" and "discounted" 
are synonymous. Therefore capital value is the discounted net 
value of future income. Finally, since all future income is 
included in present value, capital value is the sum of the dis- 
counted values of all items of future net income. This definition 
holds good whether the income is received at regular daily, 
monthly or annual intervals, or at intervals of two or more, 
even of 100 years, or is irregular in amount and paid at irregular 
intervals. 

An example of regular annual income is the interest on a 
money loan. This interest, capitalized, corresponds to the value 
of the loan of capital. This relation established between capi- 
tal and income through the rate of interest (§ 38) is the means 
of determining the capital value of all other forms of property. 

For money alone the value of the capital and of its use deter- 
mines the value of the income or rate of interest, and the value 
of money is neither raised nor lowered by fluctuations in the 
rate of interest. 

For other property the relation is: 

1. Capital or property earns income. 

2. The value of this income is appraised. 

3. This value is then discounted to obtain the value of the 
capital. 

4. The "rate of interest" is the measure of discount. 

The term "capital value" has so far found no place in the 
literature of forest valuation. Instead, such authorities as 
Schlich have translated continental terms into the English 
"expectation value." This term is descriptive of the fact 
that such values are based on future expectations, not fully 
determined; but it is open to objections, since it conveys the 



40 FOREST VALUATION 

impression that such values are different or obtained in a different 
manner from the capitaHzed values computed for all other forms 
of property. On the contrary, the process is identical and it 
would be a distinct advantage to recognize this fact in terminol- 
ogy. A third term, also identical in meaning with the two above 
mentioned, is "capitalized rental value," sometimes abbreviated 
to "rental value." Two objections to the term "rental value" 
are that it may be confused with rent, which is only one form 
of income, and that it may be taken to mean the value of one of 
the current or periodical payments of income instead of its 
true meaning, which is the sum of the discounted values of all 
items of future income. The term "capitalized rental value" 
seeks to emphasize this latter meaning, but the use of the word 
"rental" might be taken to mean that such values are deter- 
mined only for property producing income at regular intervals. 
Since it makes no difference what the character or interval of 
payment is, the term "capital value" is the most comprehen- 
sive. The one great objection to this term is that the word capi- 
tal is commonly used to denote the amount of an investment, 
or the total funds furnished by capitalists (§§ 12-13), ^^^ is in this 
sense alHed with cost rather than value of assets (§ 73). Were all 
assets in the form of money, this would make no difference (§62), 
but as cost and value for other assets diverge widely, some 
term should be used which is clearly understood as referring to 
value rather than cost. Another possibility is the term "income 
value," or "capitalized income value." "Income value" is 
open to the same objection urged against "rental value," — that 
it might be understood to mean the value of one year's income, 
or of one payment. "Capitalized income value" comes nearest 
to fully describing the value indicated and the means of ob- 
taining it. 

The valuation of forest property differs from that of property 
earning annual income only from the fact that the income may 
occur at intervals separated by long periods. Hence the tend- 
ency, expressed by the term "expectation value," to emphasize 
this "expectation." As will be shown in Chapter V, the formulae 
employed in the capitalization of annual and of intermittent 



VALUATION OF ASSETS 41 

income, such as is received from forest crops, are identical in 
character, and it is more important to recognize this essential 
similarity than to seek to differentiate forest valuation from other 
forms of appraisal. In the text, the synonymous terms "capital 
value" and "expectation value" wUl be used interchangeably, 
rather than the more cumbrous term "capitalized income 
value." 

63. Future Prices and Values. — The determination of 
capital value rests upon the ability of the appraiser: first, to 
ascertain the amount and character of the income, its duration 
and the total for the entire life of the enterprise; and second, 
to appraise the probable value of this income for the time when 
it is received, by a conjecture as to prices for the future products 
(Chapter XII). But the future is shrouded in uncertainty, 
which becomes more impenetrable the longer the period over 
which such predictions must extend. The past is an open 
book. The knowledge thus obtained by experience is the guide 
in the process of appraisal. It is comparatively easy to deter- 
mine the probable productiveness of property for any business 
which presents the results of past experience. In new and 
untried ventures this is uncertain. But future prices are far 
more of a problem, since they are the resultant of the complex 
of all the economic forces of society. Attempts may be made to 
predict changes in prices, due either to changing price levels 
based on fluctuation of the value of money, or changes in the 
supply and demand for the specific product. Such predictions 
can only be based on present tendencies interpreted in the light 
of past, especially recent, experience. 

When reliable authority is lacking for prophesying the prob- 
able nature and amount of changes in prices, although they are 
certain to occur, the appraiser is forced to accept present prices 
as the basis for future income. This principle finds its expres- 
sion in appraisals for damages, when speculative increase in 
future income is not admitted in valuations. 

64. Future Expenses. — The net present value of income is 
equal to the margin over future expenses (§ 10). These future 
probable expenses must be appraised as carefully as income. 



42 FOREST VALUATION 

Most elements of expense can be judged by past costs for similar 
undertakings. Future expenses may and will vary from pres- 
ent standards, for part of this expense is determined by prices, 
part by wages and part by legislation and taxation. Uncer- 
tainties regarding the trend of any of these elements of cost 
interfere with the accuracy of the appraisal of value. A fruit- 
ful source of uncertainty is future taxation. Legislation tending 
to substitute a definite arrangement for this fluctuating item 
is a great aid in appraising the value of forest property. 

65. The Time Element in Capital Value. — When once the 
future income and future expenses have been appraised, the 
determination of the capital value of the property is a mathe- 
matical calculation, dependent on the rate of interest chosen as 
the basis of comparison between the present and the future 
values involved. Each item of income is discounted for the 
period of time intervening between the present moment and 
the receipt of the income payment (§ ii). The sum of these 
values equals the amount of money which is equivalent in pres- 
ent value to the expected future income. The property is there- 
fore considered as having this value. For this " time difference " 
in value the rate of interest is the measure. In the same way, 
future expenses are discounted to get net value. 

The greater the time interval between the present moment and 
a future transaction, the less will be the importance of this trans- 
action when discounted to determine its present money value. 
The net capital value of property is practically determined by 
events occurring within the next fifty years, not merely because 
these events can be more accurately prophesied, but through the 
operation of the factor of discount, based as it is on the laws of 
compound interest. Not only are profits that are deferred for 
fifty years of httle significance to the investor (§41), but the 
future values themselves are correspondingly small when viewed 
from the present standpoint. The immediate future occupies 
the minds of men and its relative importance is mathematically 
expressed in discounting to obtain capital values. 

66. Effect of Rate of Interest on Capital Value. — The rate 
of interest is a barometer which measures the fluctuations that 



VALUATION OF ASSETS 43 

occur between the relative values of future and present income. 
An increase in this rate, or measure, increases the difference in 
values due to this time element. The greater this difference, the 
smaller will be all capital values. A permanent doubling of the 
rates of interest would diminish the value of productive capital 
to one-half its former worth. This premise is based on the eco- 
nomic facts discussed in Articles 60 to 64, which refer value 
directly to future income. High rates of interest indicate risk, 
unsettled conditions and instability of character, and are thus 
directly related to influences tending to depress property values. 
Low rates of interest correspondingly raise the capital value of 
property, by diminishing the loss or discount necessary in arriv- 
ing at the present value of the future income. 

67. Uncertainty of Capital Value. — The premise that value 
is based wholly on future net income is sometimes questioned, 
because of the uncertainty which surrounds every element of 
future occurrence. The determination of value on this basis, 
by mathematical deductions, is a guess, to the extent that these 
future elements are subject to change. Yet every sale of prop- 
erty is the result of a guessing contest as to these future ele- 
ments, rather than a calculation of past costs. As two minds are 
better than one and as the guess is made the basis of an actual 
exchange of property, a sale as soon as it is effected becomes a 
new indicator or basis for the next guess. The uncertainty of 
future values is identical in nature with other risks incurred in 
business and adds the element of chance which becomes the basis 
for practically ^11 forms of speculation. The difference between 
''legitimate" and "speculative" value lies merely in the degree 
of uncertainty surrounding the future conditions upon which the 
guess as to present value is based. The value of bonds fluctu- 
ates but sUghtly and then only because of changes in the "rate of 
interest," for the income is fixed and secure and the price or 
value of the bond is easily calculated mathematically by use of 
the desired rate of interest in discounting this income. By 
contrast, the uncertainty and fluctuation in the value of indus- 
trial stocks is due to a corresponding uncertainty regarding 
future dividends. 



44 FOREST VALUATION 

68. Independence of Capital Value and Past Outlay or Cost. 

— It is essential to thoroughly establish the idea of this inde- 
pendence of capital or expectation value from all elements of 
past cost. It cannot be said that past costs are without in- 
fluence on value. In most cases they have been the direct means 
of creating this value. This leads to the erroneous conclusion 
that such costs are identical with value or are value. The 
fallacy of this idea is easily shown. Cost is an individual outlay. 
Value is the product of social conditions. Costs are undertaken 
in order to obtain value and, when contrasted, are negative 
where value is positive. 

To illustrate: Two parcels of land are acquired and cleared 
at an expense in each instance of $25 per acre. One tract 
has such poor soil that it will raise nothing of value and cannot 
be sold for $5 per acre. The other is suitable for truck gar- 
dening and eventually sells for $500 per acre. Such variations 
in value, entirely independent of cost, may be caused by differ- 
ences in location or by the development of new crops or new 
markets. All such fluctuations are due directly to the prospects 
for future income. 

The true relation between cost and value is that between a 
means and an end. The cost is assumed for the purpose of 
obtaining income and the value is derived from the prospect 
of this income. If the outlay has been effectual in insuring 
the future income the rise in value will follow. If the outlay 
is ineffectual for any cause, chiefly through errors of judgment 
or through incompetence, there will be no corresponding increase 
in value. On the other hand, value will increase and decrease 
from social and economic causes not even remotely associated 
with the owner's outlay. For these reasons it must be accepted 
that past cost or outlay, while it may furnish useful information 
for the calculation of value, does not determine value. 

69. Effect of Capital Value on Sale Value. — Sale value 
depends directly upon the demonstrated ability of property 
to earn income. Whenever this earning capacity is uncer- 
tain, especially if it appears probable that it may increase in the 
future, sale values move in response to the guesses of those 



VALUATION OF ASSETS 45 

who exchange property, as to the probable future income. 
Inflated ideas of future income, if commonly accepted, result in 
inflated sale values, as instanced in real estate booms, high 
values for western fruit lands and flurries in mining stocks. 
Could sound, reliable information regarding the possible future 
income from property be a matter of common knowledge, 
inflation of values would become very difficult. Occasionally, 
by rapid development of a region, values which at first seemed 
high materialize by the assurance of income resulting from 
this increase in population. More often the boom is overdone, 
and sooner or later, values coUapse to a level corresponding to 
the measure of income possible. In every case the sale value is 
a crude attempt at approximating capital value, and the disa- 
greement between them is due to ignorance of the investing 
public as to the true present value of the possible income. 

70. Effect of Capital Value upon Appraised Value. — The 
appraiser must therefore take into account the actual sources 
of value in appraising property in order to check the sale value 
and detect any glaring discrepancies between the reasonable 
capital value of the net income and the price asked for the 
property. If the owners of wood lots are selling their timber at 
one-half to one-third of its real value, because they are ignorant 
of both the quantity of standing timber they possess and the 
current prices for stumpage, or if these current prices mani- 
festly are so low that the purchaser is able to make a very large 
profit, the appraiser can go back of sale values and determine 
the value of such stumpage directly from income (§61). Where 
no sale values exist, the determination of capital value is his 
only recourse and is fully satisfactory. 

71. Inflation of Capital Values. — Value thus depends upon 
future income which may never materialize. On the chances 
of obtaining this income, investors are willing to purchase prop- 
erty at values computed by discounting these chances. The 
rate of income earned on the past cost or invested capital of the 
owner does not fix the price of the property. The amount and 
value of this income are the determining factors. The price is 
determined by discounting this value, using a rate of interest 



46 FOREST VALUATION 

which is satisfactory to both the purchaser and owner. Should 
a business be sold which represents an investment of $50,000, 
and earns a net income of $25,000 per year, or 50 per cent on 
cost, the purchaser would probably be satisfied with 20 per cent 

per year. The price will then be -^ , or $125,000, and the 

^ .20 

former owner has exchanged his income of $25,000 for capital 
on which he in turn must earn 20 per cent in order to be as well 
off as before. 

In the large operations of modern finance, especially in the 
formation of trusts and transportation monopolies, it was con- 
sidered that unlimited opportunities for future income would 
be created by the control of prices and railroad rates. This 
belief was then capitaHzed on a generous scale. The final step 
was to sell these securities to the public, thus realizing, for the 
original owners, the capitalized income which had not been 
earned. This inflated income must now materialize or the 
value of these investments will correspondingly diminish, as 
has been the case with many such ventures in the recent past. 

72. The Regulation of Capitalization. — It is possible to 
prevent the fraud and burdens of over-capitalization by giving 
to states or the national government the power of supervision 
over such semi-pubhc operations. Since income is the key to 
capitalization, the exaction of extortionate rates or prices should 
be checked. Capitalization may also be regulated to conform 
to the reasonable requirements and to the true earning power 
of the business. The effect of such regulation will cause dis- 
proportionate differences between the capital value placed 
upon a business and its actual cost, to shrink to reasonable 
proportions, and the balance sheet to show a margin of profit 
more in keeping with the best interests of the public from whom 
must come the income upon which these values rest. 

73. The Problem of the Balance Sheet. — Accounting prac- 
tice is based on an equation in which 

goods or assets = Habilities + proprietorship. 
The left-hand member of this equation represents the tangible 
and intangible assets, at book value, or whatever value is 



VALUATION OF ASSETS 47 

adopted as correct according to the conditions and principles 
employed in determining such values. Accounts receivable 
and debts owing to the business are part of the assets. 

The right-hand member represents the capital paid in plus the 
borrowed capital. Debts owed by the business and accounts 
payable plus borrowed funds constitute the liabilities. 

In balancing the equation, the "value" of assets is first 
determined. The liabilities are rigid, therefore the balance 
represents the proprietorship. When this is originally expressed 
as capital stock, an excess of value is shown as surplus, while a 
deficit is carried to the left member to balance. 

Changes in the status of the business, which are constantly 
occurring, take one of two forms; a change in value of capital 
resulting from net income or loss, or a change in said value 
independent of such net income or loss. The cash for the pur- 
chase of assets must come either from the proprietors as addi- 
tional capital, or from surplus derived from income. On the 
other hand, sales are mere exchanges, bringing in an equivalent 
asset in cash. 

It is evident, then, that the assets are increased only by 
Additional capital invested by proprietors. 
Net income, from 

Excess of sale value over cost of assets. 
Revenue from use of assets. 
Appreciation in value of assets. 
The last item is a potential income, which may or may not be 
eventually realized. In the same way, assets are decreased by 
Withdrawal of capital by proprietors. 
Losses or destruction of assets not insured. 
Dividends. 
Expenses. 
All items of current income or expense effect a corresponding 
change in the net value of the capital, but as the balance sheet 
is not usually made up of tener than once a year, these items are 
carried in the profit and loss account, and only the surplus or 
deficit entered in the balance sheet. 

The commercial balance sheet attempts to show, first, the 



48 



FOREST VALUATION 



status of the assets, and second, the relation existing, as a result 
of this status, between assets and proprietors. 

The problem of the balance sheet lies in the treatment of 
potential income, and its effect on the value of the assets. As 
long as the assets are entered at cost, and income appears only 
after it has been actually received, no potential or unearned 
profits appear in the balance. On this basis, the excess of 
annual costs over annual income may be added to capital as 
cost of assets, as is permitted in railroad construction (§ 57), and 
by the government in computing the income tax (§ 162). Un- 
earned interest on such costs would be excluded in a balance 
sheet. 

But if the assets are revalued, at "actual" value, based 
perhaps on present increased sale value, but due entirely to 
increased prospects of income capitalized as expectation value, 
the alteration of the value of the assets, thus justified, indicates 
an apparent profit to the owners exactly equalHng this increase, 
not yet realized nor available for the payment of dividends. 

Not only does the balance sheet fail to distinguish between 
actual and potential profits, but it entirely ignores the element 
of time in indicating the relative value of the profits earned, 
compared with the capital invested. 

The fundamental relations exhibited in the balance sheet, 
and its connection with the profit and loss account, may be set 
forth in the following framework. 

Balance Sheet 
Assets Liabilities, 

Proprietorship 

+ - - + 



Cash. 

Capital assets in 
form of goods 
or property. 

Deficit. 




Capital paid in. 

Borrowed capi- 
tal or liabili- 
ties. 

Surplus. 



The diagram corresponds to an equation in which the opposite 
sides may show both plus and minus items. A minus item, by 
transfer from one side to the other, becomes plus. The items 
included in each subdivision represent a separate equation. 



VALUATION OF ASSETS 



49 



CHANGES IN STATUS DURING YEAR 

I. Capital Account 

a. Deductions from Capital 

I. Depreciation 



+ 


- 




- 


+ 




Losses not cov- 




Corresponding 






ered by insur- 




reduction in 






ance. 




value of pro- 






Depreciation in 




prietorship 






value not off- 




constituting 






set by income 




a loss of cap- 






or deprecia- 




ital or of sur- 






tion fund. 




plus. 







2. Withdrawal of Capital 






Withdrawal of 
cash or other 
assets by 
transfer to 
proprietors. 


= 


Cancellation, 
or reduction 
in value of 
capital 
stock. 





These withdrawals may be induced by the sale of certain of 
the capital assets, or by their depreciation in value. Instead of 
creating a depreciation fund, the investment in a business may 
be steadily reduced. This would be the course pursued in 
lumbering, should it be found impossible to reinvest the income 
in new timber stumpage or otherwise continue the operation. 
The cancellation of bonds issued against standing timber must 
keep pace with the cutting of this timber. 

b. Additions to Capital 

I. Additional Investment 

+ - - + 



Purchase of ad- 
ditional as- 
sets. 

Cash. 



Additional capi- 
tal paid in. 



2. Income 



Depreciation 
fund. 

Increase of sur- 
plus. 




Net income 
(gross income 
minus annual 
expenses, in- 
terest and divi- 
dends) trans- 
ferred from 
profit and loss 
account. 



50 



FOREST VALUATION 
3. Capitalized Expenses 



Increase in book 
value, i.e., in 
cost of capital 
assets already 
owned. 




Additional capi- 
tal to meet 
deficit caused 
b y excess of 
expenses over 
income. 



This last transaction consists in marking up the capital assets 
on the basis not of value, but of cost, to coincide with the addi- 
tional capital advanced to meet annual expenses in absence of 
revenue. Normally the deficit would appear as such in the 
balance sheet and not in the capital account. 

The appreciation in value of capital, or unrealized profits, 
requires no corresponding investment, and should be distin- 
guished from increase in cost by a separate account. 

4. Appreciation of Assets 
+ - - + 



Appreciation or 
marking up of 
value of capi- 
tal assets. 




Corresponding 
increase in 
proprietorship 
representing 
potential prof- 
its. 



II. Profit and Loss Account 
This account records the cash outlay and income during the year, and 
its balance, indicating a net income or deficit, is then transferred to the 
capital account, and appears in the balance sheet. 

+ - - + 



4. Deprecia- 
tion fund. 






1. Cost of cap- 
ital assets. 

2. Annual ex- 
penses. 

3. Interest on 
borrowed 


Gross income, in- 
cluding sale of 
capital assets. 


6. Additions to 
surplus. 






capital. 
5. Dividends. 





Item I represents cost of assets sold, and this amount is 
credited to the capital asset account. Item 2 includes 
the current expenses of operation including taxes. Item 3, 
interest on borrowed capital is met before further disposition 
of income is pemiitted. In item 4, the depreciation fund thus 



VALUATION OF ASSETS 



51 



appropriated from income offsets the loss from this source in the 
capital account. Item 5, dividends are then appropriated, and 
the remainder of the annual income (item 6) represents profits 
remaining in the business. 

A deficit, instead of a net income, occurs if the gross income 
is insufficient to cancel the first three items. When a regular 
annual provision is made for depreciation this may also cause 
a deficit. In case this deficit occurs, it results either in dimin- 
ishing the surplus, or the value of the proprietor's equity, or 
else it is considered as a natural and legitimate cost to be added 
to capital expenditure. This difference in the point of view 
coincides with the difference between enterprises yielding annual 
income and investments on which income is naturally deferred 
for longer periods. 

The failure of the commercial balance sheet to fully inform 
the investor as to the true economic status of his business, for 
the reasons mentioned (page 48), suggests a supplementary 
statement, in which the factor of time, and the increase in value 
of assets due to future or potential income, may be expressed. 
Such a statement is merely a prospectus or forecast, but will be 
of great value if its true character is clearly explained. Its 
principal use is found in connection with a business in which the 
actual returns are deferred rather than annual. 



III. Prospectus or Forecast 



Debit 



Credit 



+ 



+ 



Expectation 
value of future 
income, capi- 
talized as val- 
ue of assets. 

Potential profit. 



Future costs to 
be subtracted 
from income 
previous to 
capitalization. 



Past income. 

Interest cred- 
ited on past 
income. 



Total cash in- 
vestment for 
all purposes. 

Interest defer- 
red on cash 
investment. 

Potential loss. 



To obtain this last balance, the cost of assets must be shifted 
to the "credit" column, thus comparing cost with capitalized 
or expectation value and revealing the potential profit by which 
the true economic status of the business may be gauged. 

The sources of confusion in the treatment of assets by 
accountants are now revealed. Costs and value are diametri- 



52 FOREST VALUATION 

cally opposite in character, yet custom and the practical 
necessities of commercial accounting compel a consolidation or 
compromise between these elements, as a result of which the 
valuation of assets is sometimes based on cost, with or without 
" expenses," sometimes on capital value, and often on both 
cost and value. Sprague * ' both sums up and explains this 
practice by the statement: "The aspect of assets as the present 
worth of future services (capitalized income)! is entirely based 
on opinion, while the aspect which regards them (assets) as the 
resultant of services (cost) is based upon facts." 

It is evident that the proprietor is at liberty to compute his 
potential profits by capitaHzing future net income on any basis 
which he sees fit, and may charge against this value a cost on 
which he adds the unearned interest on his capital. He may in 
this manner satisfy himself as to his economic status, and deter- 
mine whether to sell, buy, or continue to operate. But in pubHc 
accounts a limit must be placed both upon inclusion of costs 
not actually incurred, and of profits not yet realized. Hence 
the full and perfect expression of economic status is seldom per- 
mitted or secured by the commercial balance sheet, and must 
be left to supplementary calculations in the nature of forecasts. 

In this economic comparison, the proprietary or right-hand 
member of the ordinary balance sheet does not appear, and the 
account deals entirely with the material assets. The balance 
is struck between past costs, with interest, less past income, 
and future value, discounted, less future expenses. Instead of 
being upon the same side of the equation, necessitating an 
arbitrary choice between absolutely opposite elements, the 
equation lies between cost and value, and the balancing quantity 
is the potential or unearned profit or loss, expressed as capitalized 
or expectation value. 

The incorporation of a portion of this potential profit into 
the regular balance sheet, previous to actual sale of the business, 
is an action dictated entirely by motives of expediency. 

* " The Philosophy of Accounts," by Charles E. Sprague, 54 West 32d St., New 
York, p. 41, Art. iii. Published by author (at above address). 1908. 
t Material in parentheses inserted by author. 



CHAPTER V 
FORMULA OF COMPOUND INTEREST 

74. The Discount Factor. — The mathematical relation be- 
tween present and future values is expressed by formulae. By 
substituting the desired rate of interest in the formula the ratio 
is found by which the one value may be converted into the other. 
This ratio may be termed the "discount factor." 

75. Rentals. — The term "rental" is used to denote a 
definite sum recurring as income at regular intervals. The 
interval may be of any length, even one hundred years, provided 
the payment is assumed to recur periodically. Since income 
to one person means outlay to another, the amount of an expense 
occurring at regular periods is obtained by treating it as a rental. 
The sum of the future values of a series of payments consti- 
tuting a rental must frequently be determined, as well as the 
discounted or present value of this sum. 

The formulae needed in valuation are those which will deter- 
mine : 

The future value of single sums. 

The present value of future sums. 

The future value of the sum of rentals. 

The present value of the sum of future rentals. 

The ratio between present and future values. 

76. Future Value or Cost of Single Sums. — 

V = value of capital or sum. 

Vq = value at beginning of period. 

Vn = value at end of period. 

VijVo = value at end of years indicated by numeral. 

n = period intervening before final reckoning. 

p = rate of interest adopted. 

P 
-^— = o.op, mterest expressed decimally. 

lOO 

S3 



54 FOREST VALUATION 

The expression o.op is an arithmetical term, in which the letter 
p is substituted for the numeral representing the rate of interest. 
For a given rate, as 4 per cent, the expression reads 0.04; for 10 
per cent, it reads o.io, 

o.op is the ratio between capital and interest for one year. 
Therefore i + 0.0^, or i.op, is the ratio between the capital at 
the beginning and end of the year, assuming that the interest is 
added to the principal. 

Fi : Fo : : i.op : i. 
Fi = Fo X i.o^. 

At the end of the second year 

V2 :Vi : : I.op : 1. 
F2 =Fi X I.op 

= (Fo X i.o^) I.op 

= Fo X 1.0^2^ 
F3= (FoX I.op'') I.op 

= Fo X I.op'' 
and F„ = (Fo X I .op^-^) i .op 

= Fo X i.op^. ■ (I) 

This formula is used to determine the accumulation of cost on 
an investment which does not produce income until the close of 
a stated period. In such a cost account (§§ 25 and 36) all in- 
vestments are charged with interest. Sums representing expend- 
itures which occur only once and cannot be treated as rentals, 
as, for instance, the cost of planting trees, are totalled for n 
years by this means. 

All formulse dealing with future values of present sums show 
also the present cost of past expenditures. They reckon forward 
from beginning to end of an investment. 

77. Present, Expectation, or Capital Value of Future Sums. — 
In computing future sums, the value at a future period has no 
special significance until it is discounted to the present. 

If F„ = Fo X i.o^" 

then ^o=-^„- (II) 



FORMULA OF COMPOUND INTEREST 55 

The arithmetical equivalent of ^ may be expressed as a 

decimal. 

Discount formulae are used in valuation of assets. The 
discounting of future "profits" or net income is identical with 
the determination of capital value. There can be no value in 
excess of this discounted net income (§62). 

To obtain this net present value, future costs may be first 
discounted and then subtracted from discounted gross income. 
Or this subtraction may be made at any future period and the 
net income discounted. If the values are properly computed 
to the same year, before striking the balance, the discounted 
results are identical. For instance, an expense c occurs in the 

year d, which Hes between the years o and n. 

c 
The present value or equivalent of c will be ^ • 

The future equivalent oi c at the end of the year n will be 
c X i.o^""'^, since n — d is the period over which interest on c 
would accumulate. 
The present equivalent of c X i .o/>"~'^ will be 
c X i.op""'^ _ c X i.o/>" _ c 
I. op" ~ 1.0^"+'^ ~ i.op'^ 

Hence, to determine the net present value of future income, 
future expenses may be computed forward to the year in which 
the income is received, and subtracted from this income, and the 
resultant net income discounted to the present. This accom- 
pHshes the same purpose as discounting each item of expense 
to the present before subtracting it from gross income. The 
choice of these methods is merely a matter of convenience. 

78. Use of Logarithms and Tables. — The arithmetical 
equivalents of these formulae are calculated by the use of loga- 
rithms. The numeral representing the desired rate of interest 
is substituted for p, and the number of years in the period for 
n. For 4 per cent and 50 years, i.op"' becomes 1.04^". The 
logarithm of i .04 is multipHed by 50. The result is the logarithm 
of 1.04^", from which the ratio is obtained. In the case cited, 
the ratio is 7.1067, which indicates that $1.00 will increase in 



56 FOREST VALUATION 

value to $7.1067 if placed at compound interest at 4 per cent for 
fifty years. 

The value of all other formulae are derived from the expression 

i.o/)". The values for discount, , are obtained by reducing 

the fraction to a decimal. In the above case, — gives a 

7.1067 

discount factor of 0.1407, which means that $1.00 payable in 
fifty years has a present value, at 4 per cent, of $0.1407. 

These values may be expressed in tables, which make such 
calculations unnecessary. (Table VI, appendix.) 

79. Future Value of Temporary Annual Rentals. — The 
future value, or cost, of a rental continuing for a temporary 
period represented by n annual payments, equals the sum of 
all these items plus interest upon each from the date of pay- 
ment to the end of the year n. 

The payments are regarded as occurring in each instance at 
the end of the year, although they might be made during the 
year. The final payment thus incurs no interest charge. 

Let r = annual rental. 

Then, final rental for year n = r. 

Rental for year n — 1, in year n = r X i.op. 

Rental for n — 2, in year n = r X i.op'^. 

Rental for first year, in year n = r X i.o^"~^ 

These terms form an increasing series showing a geometrical 
progression. The ratio of increase or multiple is the factor i.op. 
The sum of these terms gives the total value or expense of the 
rental at the end of the period. The calculation of these separate 
values is unnecessary. The sum may be obtained by formula. 

Let Vr = total value of rental. 

(i) Vr=r-^r{i.op)-\-r{i.op'')+r(i.op^) -}-■ • • -\-r{i.op''-^). 

Multiply the equation by the ratio i.op. 

(2) Vr{i.op) = rii.op)+r{i.op-)-{-rii.cp^)-\ hr(i.o/>"). 

Subtract (i) from (2). 

Vr (i.op) - Vr=r (i.op'') - r, 
Vr (i.op - 1) = r (i.op" - i), 

I.op — I 



FORMULA OF COMPOUND INTEREST 57 



Since i.op — i = o.op, 



V, = iSi^H^A (III) 

O.op 



r 



(i.o^"- i). 
o.op 

Outlay for fire protection or sums paid annually for adminis- 
tration serve as examples of annual rentals. As income we may 
have receipts from grazing or hunting privileges. The above 
formula holds good only during the period that such rentals 
remain equal in amount and value as is the case with actual 
rent. Should they fluctuate annually, each item must be sep- 
arately computed. 

If rentals remain the same for a period and then rise or fall 
to a different level for a second period, the above formula is 
used to compute the total to the end of the first period. This 
value then bears interest for the remaining period as a definite 
sum (I), and the value of the new rental n for this second 
period is computed in the same manner as before and added to 
the total. For two periods termed a and h this reads: 

^^^ u(i.or-i) > ,^ >-,(i.o/-i) ^ 

( o.op ) o.op 

80. Formulae for Geometric Series. — In the series whose sum 
is obtained by Formula III, the ratio i.op is greater than i, 
which gives an increasing series. 
Let g = first term of series. 

q = ratio or multiple (such as i .0^) . 
Q = sum of series. 
Then, by demonstration above (III), 

C=«-<^. (Q.) 

The sum of future values of rentals forms such a series. 

Should the ratio be less than i, each succeeding term will be 
diminished in value, which gives a decreasing series. 

The sum of this series is obtained by the same formula, but 
a more convenient form of expression, obtained by multiplying 
both numerator and denominator by — i , is 

()=«(if^). (Q.) 



58 FOREST VALUATION 

The sum of present or discounted values of rentals forms such 
a descending series. 

These formulae apply either to temporary rentals, with a 
limited number of terms, or to perpetual rentals, with an infinite 
number of terms. 

For an infinite increasing series 

Q = ^ ^^^ ~ '-* = 00 (infinity). (Q3) 

q- I 

For an infinite decreasing series, since the value of §'" dimin- 
ishes in direct proportion to the exponent used, 

g* = o. 
Therefore 

Q=^-i^^^ = ^. (Q.) 

1 -q I -q 

81. Present, Expectation, or Capital Value of Temporary 
Annual Rentals. — Let R = present, expectation, or capital 
value of the sum of a rental. 

Should each rental be discounted to the present by Formula 
I, the sum of the resulting terms is 

i.o^ i.op^ i.op^ I.O/>" 

Applying Formula Q2 for the summation of decreasing 

temporary rentals, 

r 

^ i.op 

I 

q = » 

\.op\ I.op'') 



R 

I — 



I.op 
Multiplying numerator and denominator by i.op X i-o^", 

r (i.op"' — i) 



R = 



{i.op — i) i.o^" 
r (i.op" — i) 
o.op X I.op" 



rd-op"-!) (IV) 



FORMULA OF COMPOUND INTEREST 59 

The same result may be obtained by discounting the final 
future value of the sum of these rentals to the present (II). 

This future value Vr = ^^^•°^" ~ '^ . 

0.0^ 

Hence rji.op'' - i) i ^ rji-op" - i) 

o.op I. op" o.op X I. op" 

Since capital value is the net value of income discounted to 
the present, the application of this formula is evident. It may 
be used to discount either annual income or annual expenses. 
Should the two occur simultaneously, only the net annual 
profit or loss is thus discounted. 

82. Future Value of Temporary Intermittent Rentals Due 
First at u Years, and f Times at Intervals of n Years There- 
after. — A rental which occurs at intervals greater than one 
year is termed intermittent, although if the interval is regular 
it does not differ in character but only in degree from annual 
or monthly rentals. 

Let n = period between rentals. 

t = number of payments expected. 
nt = total period covered by the investment. 
/ = intermittent rentals due at intervals of n years. 
Vr = total value of intermittent rentals at end of period. 

The future value of the sum of these rentals, if computed in 
the year of payment of the final rental, is 
Final payment = r', 

Payment, n years preceding = r' {i.op"), 
Payment, 2 n years preceding = / (i.o/>^"), 
First payment = / (i.o^^'"^)"). 

By use of Formula Qi, the sum of these terms is found by 
substituting the ratio i .0/)" for q and the factor t for n. 
The formula then reads: 

/(i.or-i). (V) 

i.o^" - I 

Either income or expenses which terminate at a definite 
date are far more apt to occur annually than at longer intervals 



6o FOREST VALUATION 

(III and IV), and if intermittent and terminating, such as a 
succession of thinnings from a crop of timber previous to final 
cutting, they are also apt to be of different values, requiring 
separate valuation. If assumed to be equal in value, they may 
usually be assumed to recur perpetually (IX). 

83. Present, Expectation, or Capital Value of Temporary Inter- 
mittent Rentals, Due First at n Years, and t Times at Intervals 
of /* Years Thereafter. — The present, expectation, or capital 
value of intermittent rentals limited in number is found as 
in the case of annual rentals. 

The series decreases. 

For rentals due first after n years and / times at intervals of 

n years thereafter, this series is 

/ / / ' 

y Y Y r 

R =-^ + -^T77 + — ^+ • • • + 



I.O^" I.O/>-" I.O^"*" l.Op' 

Then (Q2), 



q = 



Q = 



i.o/>" 
I 

I.O/>" 
/ 

r 



I 
I — 



I. op" 
Multiplying numerator and denominator by i.op" X i.op"', 

^^ /(i.or-i) (VI) 

ii.op" - l) I.O/>"' 
The same result is obtained by discounting the future value 
of the series (V) to the present (II) using the factor as 

the substitute for 



i.o/>" 

/(i.o/>"' - i) I ^ / (i.o/?"' - i) 

~ I.O/?" - I i.op"' ~ (i.o/>" - l) I.O/?"' 

84. Future Value of Temporary Intermittent Rentals, Due 
First in a Years, and t Times at Intervals of n Years There- 
after. — When the value of the sum of temporary rentals is 



FORMULA OF COMPOUND INTEREST 6l 

determined for the date of the final payment, falling in the 
year nt, the interval elapsing subsequent to this payment is 
zero. When this payment falls at some previous date, -a, the 
total value at that date accumulates interest during the remain- 
ing period. This period is equal to n — a years. 
The series forming the sum of the rentals is 

Vr = r' (i.o/>"~") + / (i.o/?-""") • • • + / (i.o/>'"-°). 

By use of Formula Qi, substituting the ratio i.o/>" for q, and 
the factor t for n, this becomes 

^ / d.or' - i) i.or- . (VII) 

I.O/>" - I ^ ' 

By multiplying Formula V by i.o^""" (see Formula I), the 
same result is obtained, 

85. Present, Expectation, or Capital Value of Temporary 

Intermittent Rentals, Due First in a Years, and t Times at 

Intervals of u Years Thereafter. — The present value of the 

r' 
first payment, due in a years, is (II). The period a may be 

of any length and may exceed n. The present value of subse- 
quent payments diminishes by the constant ratio ^^ , form- 
ing the series 



To obtain the sum of present values (Q2), 
r' 



q = 



I. op" 
I 



Q^^ 



i.o/?" 

i.o/>"\ i.o/>"7 



i.op" 



i.op' 



- = /{i.op-'^). 



62 FOREST VALUATION 

Multiplying numerator and denominator by i.op" X i.o/>"', 

/(..or-i)i.°r- . (VIII) 

(i.op" - i) i.o/?"' 
This formula is also derived from Formula VII by discounting 

the final value to the present (II), substituting — for -• 

i.o/>"' I. op" 

Formulae V to VIII are seldom used in forest valuation 
(§82). 

86. Present, Expectation, or Capital Value of Perpetual 
Rentals. — Under the assumption that a rental is perpetual 
(§80), the intermittent rental r, payable every n years, forever 
will have a future value equal to infinity (go). 

Its present value (Q4) is 

/ 

I 

a = } 

^ i.op'' 
.J 



C = ^£^ 



I — 



I.O^" 

R = '- . (IX) 

i.o^" - I 

If the first rental is paid in the year a instead of at n years, 
as in case of revenue from thinnings, the present value of the 
sum of a perpetual series due every n years thereafter (Q4) is 



i.op" 

I 
i.o/?"' 



Q = -l^ 



I — 



i.o/>" 

I.O^" - I 



FORMULA OF COMPOUND INTEREST 63 

But should the period of discount lie between the year a and 
the final year n, when the crop is harvested, as it does when 
the value of growing timber is computed at a years, this formula 
(Q4) is 

* I. op"-" 

_ I 

^ ~ I.O/?"' 

/ 



I 

I — 



I.O/>" 



iJ = ^^%5i^. (Xa) 

I.O/>" - I ^ ' 

When the first rental is due in the present year, the series 
becomes 

R=r' +-^ + -^+ • • . + '' 



i.op" I.Op^" I. op" 



Q = 



I 
i.op" 



^ _ /(l.O/>") ^ 
I.O/)" — I * 



(XI) 



By separating the first payment from the series, the remaining 

/ 
terms equal (see IX), and the sum is 

R = /-h—^ • (XIa) 

I. op" — I 

An annual rental, payable perpetually, has a present, expecta- 
tion, or capital value (Q4) of 

I 



I. op 



64 FOREST VALUATION 



e = -i^ 



I 

I — 



R = 



i.op 
r 



I.op — I 
= -^. (XII) 

Formulae IX to XII are of great importance in forest valuation. 
The conception that a rental may be perpetual is difficult to 
grasp. But this is merely another way of stating that the prop- 
erty producing the rental does not depreciate in value. Grant- 
ing this premise, the receipt of income for any given period 
leaves the property capable of yielding another return of equal 
value. Since this assumption can be extended indefinitely, the 
expected income may be regarded as perpetual. 

Formula XII is customarily used to determine the money 
capital which will produce an annual income of r. If we assume 
that money remains of the same value, and nothing occurs to 
impair the integrity of the capital, it can be imagined that 
this income is perpetual. In the case of land whose fertility is 
maintained by proper methods, so that the net income does 
not represent a drain of capital, or soil depreciation, the same 
conditions are true, and the capital value of the soil may be 
found by use of Formula XII. 

This premise will hold for forest lands producing crops at 
long intervals. The trees maintain the productiveness of the 
soil. In this case, the net income, being intermittent, is cap- 
italized by Formula IX. 

For practically all other forms of investment, revenue is 
apt to be accompanied by depreciation of capital, which causes 
the income to diminish and finally terminate, thus requiring, 
instead of the simple formulae just quoted, the use of the formulae 
IV, VI or VIII for the present value of temporary rentals. 

These values are less than those obtained by or 

i.o/?" — I o.op 



FORMULA OF COMPOUND INTEREST 65 

and the erroneous use of these latter formula; leads to over- 
valuation of assets. 

87. Relation Between Future Value of Temporary Annual 
Rentals and Present, or Capital, Value of Same. — In the 

formula for future value of temporary annual rentals, expressed 

as (i.o/>"— i) (§79), the portion -represents the capital 

o.op o.op 

value of a perpetual annual rental (XII), or the capital which 

will produce an annual income of r. This formula might be 

expressed (i-o/?") • 

o.op o.op 

Y 

Substituting R for 1 

R = capital value of annual rental r. 

Then -^ (i-o/^'O - ^^ = i? X i.o/>" - R 

o.op o.op 

= R {i.op'^ - i). (Illb) 

This expression gives the sum of the compound interest, or 

deferred income, earned by the capital R in n years, and is 

obtained by computing the value oi R Sit n years at p per cent, 

and then subtracting the original capital. 

The numeral i substituted for R indicates that at any future 
period the original capital remains intact. Since the sum of 
the future values of an annual rental is thus shown to equal 
the compound interest or income on its capitalized value, the 
formula R (i.o/>" — i) may be used to compute the total cost 
not only of annual rentals, but of interest on invested capital 
whenever the capital so invested remains intact at the end of 
the period, as is the case with land. 

88. Conversion of Intermittent into Annual Rentals. — To 
convert an intermittent rental occurring every n years into its 
equivalent annual rental, it is incorrect to divide the amount 
of the intermittent rental by the factor n. The intermittent 
rental is not received until n years from date, while the annual 
rental is received in installments over the entire period, which 
makes the average period of deferred payment less than half 
as long. 



66 FOREST VALUATION 

r' 

The capital value of an intermittent rental is and 

i.o/?" - I 

of an annual rental . Since the annual income for each is 

o.op 

required to be equal, these expressions must have the same value. 

„/ 
If 



T.Op^ — I O.op 

then r = X o.op. (XIII) 

The annual rental equivalent to an intermittent rental falling 
due first at an interval shorter or longer than n is found in 
the same way by multiplying the capital values given in for- 
mulae XI and XII respectively by o.o^. The results show that 
notwithstanding the fact that the intermittent rentals are 
equal in amount and paid at equal intervals, the capital value, 
and its equivalent in permanent annual income, constantly rises 
until one of the intermittent payments is received, which at 
once diminishes this capital value by the exact amount of the 
payment. If exchanged for an annuity at this time, the per- 
manent income thus secured is the lowest for any portion of 
the period, while a similar exchange effected just previous to 
receipt of intermittent income secures the maximum annual 
revenue. 

89. The Ratio of Income or Earnings. — The "rate of inter- 
est," p per cent, is accepted as a fixed standard in computing 
cost (I); or in discounting for value (II). But when both cost, 
or investment, and income are known, the ratio of this income 
to cost represents the earnings of the capital invested, or divi- 
dends. A rate of interest can be found by which the discounted 
value of income is made to exactly equal cost, or the accumu- 
lated costs to just balance income. This rate is the per cent 
earned by the investment. 

To distinguish this rate from the "rate of interest" p, the 
term x will be used. 

X = per cent representing income earned. 



FORMULA OF COMPOUND INTEREST 67 

Then 



i.oa;" 




I. ox 


= I + o.ox, 


I + o.ox 


- v7^» 


o.oo; 


-if.- 


X 


..„(i/E 



■)• 



(XIV) 



The rate x enables the owner to compare the earning power 
of his investment with enterprises which produce annual divi- 
dends (Chapter VIII). 

Instead of solving the above equation, the value of x may be 
found by inspection of Table VI. The value of i.ox" is calcu- 
lated, and the nearest equivalent figures must be found opposite 
n years in the table. By interpolation, x may then be found to 
within one-tenth of i per cent. 



CHAPTER VI 
INVESTMENTS AND COSTS IN FOREST PRODUCTION 

90. The Business of Forest Production versus Lumbering. — 

Lumbering is a term applied to that portion of the business 
of forest utilization which begins with the removal of the forest 
products from the soil and is completed when the wood is 
placed upon the market as lumber, ties, shingles or other products. 
The stage dealing with the felling and transportation of the raw 
product to place of manufacture is termed "logging," while the 
manufacture itself is spoken of as "milling." 

Forest production is a separate undertaking, which precedes 
lumbering, and deals entirely with the growing of forest crops, 
principally wood products. Until recently, the raw material 
on which the enormous investments in logging and milhng are 
dependent, was drawn entirely from virgin stands grown with- 
out human aid or expense. Ultimately, forest production must 
rank in importance with lumbering, for under modern condi- 
tions, forests will seldom renew themselves unaided. The only 
large and complete organization of forest production as a business 
in this country at present is found in the administration of the 
national forests. The operations of certain states are gradually 
taking on a systematic form. But, as a whole, the productive 
side in the management of private timberlands has not yet 
been organized into a systematic effort, and takes the form of 
tentative or experimental measures, completely overshadowed 
by the operations of lumbering. 

Logging and milling are indispensable adjuncts to production, 
but without it they are self-destructive. These three operations 
complete the chain of effort by which the income from forestry 
is finally secured. Owners of large tracts of timber usually 
undertake to log them in order to produce income from their 
holdings, and professional lumbermen prefer to own their stump- 

68 



INVESTMENTS AND COSTS IN FOREST PRODUCTION 69 

age. When stumpage is owned, logged and manufactured by the 
same person or corporation, both costs and net profits are based 
on the total operation. Frequently an owner of stumpage will 
contract the logging and do his own milling. Both logging and 
milling may be contracted, the owner receiving the final net 
revenue from sale of lumber. Or, the owner may sell his 
stumpage, permitting the logger and mill man to make what 
profit they can. On the books of a firm operating with their 
own stumpage, a technical separation of costs is made between 
stumpage, logging and manufacture. The total profits as well 
should theoretically be distributed between these three depart- 
ments, but for practical purposes this is unnecessary. Where 
desired, the "value" of stumpage is charged as a cost against 
logging. By increasing this value, logging costs are advanced 
in the same proportion, and the profits disappear into stumpage 
values, without in any way altering their amount or character. 
But should stumpage be owned separately, and its sale constitute 
a transaction taking place between different firms, the costs and 
profits arising from sale of stumpage are actual. 

Forest production as a separate business, or even as a separate 
department of the general business of lumbering, is completed 
with the sale of the timber or products on the stump. This 
separation from lumbering is illustrated by the operations of 
the United States Forest Service, which performs no part of 
the logging or manufacturing. 

When an owner of forest property finds it necessary to engage 
in logging and manufacturing, he should separate the costs 
and profits of these enterprises from the profits on growing or 
holding his timber. Often the owner is in position to log his 
own tunber. TKis may result in securing a combined or total 
profit far in excess of the receipts obtainable from sale of stump- 
age. In general, lumbering, to pay as an enterprise, requires 
large tracts and a supply of timber which will last for a reason- 
able period, and the owners of small tracts must either sell 
their timber on the stump or contract for its manufacture. 

91. Proprietary Accounts in Forestry. — Proprietary accounts, 
showing the amount of capital invested, and the income and 



70 FOREST VALUATION 

outlay, or profit and loss in the business of forest production, will 
deal with the operations of the owner as a unit, and not with the 
stand. If such accounts are kept according to the customary 
forms, only actual cash outlay or income can be recorded. 
The expenditures might be separated into capital account for 
such items as land, and profit and loss for wages, taxes and 
other current expenses. 

Unfortunately, both for the accountant and the proprietor, 
such a business may fail to pay dividends for an extended period. 
Whether it does so or not depends upon the condition of the 
forest, for if the timber is already produced or grown, the income 
is within reach. With a young forest, or plantation, additional 
capital is required to cover every item of annual outlay in excess 
of income. Since no dividends are produced, interest on bor- 
rowed capital increases at a compound rate, actually when this 
interest is also borrowed and paid, or by analogy, when its pay- 
ment is merely deferred. 

Unless this condition is foreseen, and the enterprise floated 
without borrowing, or the loan is negotiated on the basis of 
deferred instead of annual interest, which is not customary, the 
proprietor must pay this interest or bankruptcy ensues. No 
existing custom of book-keeping will permit the charging of 
unearned interest as a cost or actual expenditure, unless it is 
paid out as above indicated. Hence, in the absence of borrowed 
funds, the accumulating "costs" represented by deferred in- 
terest (§ 36) are not shown on the books. 

For a forest investment, representing, as it usually does, 
timber in all stages of growth, some capable of yielding income 
at once, while other portions require outlay for many years, it 
will be necessary to keep a proprietary account in the usual 
form, omitting the item of deferred interest on the owner's 
capital. Such an account will eventually show net profits, 
regarding interest as income (§37), but it will not reveal actual 
"cost," nor the profits of the undertaking (§39) or enterpriser's 
gain. 

92. Cost Accounts in Forestry. — A serious defect in such 
proprietary accounts is that the value of the element of time is 



INVESTMENTS AND COSTS IN FOREST PRODUCTION 71 

wholly neglected (§11) and profits received after many years are 
shown in amount only, as though of equal value with profits 
of the year. In contrast, cost accounts (§25) seek to eliminate 
such inconsistencies and express costs in their true economic 
relation to income. This is accompKshed by the adoption of a 
rate of interest (§§ 52 and 53) by which all expenditures are cal- 
culated forward to the year when the income, for which the cost 
was incurred, is finally received (§ 23). In practice, a separate 
cost account could be kept for each stand, lot or subdivision. 
The summary or total to a given date (the present) of these 
accounts would reveal to the proprietor his exact investment, 
including the "unearned" interest. This summary should differ 
from the corresponding items in the proprietary account by just 
the amount of this interest. 

93. Investments, or Permanent Outlay. — Expenditures for 
property of a durable character in forestry are confined to land 
and to permanent roads, houses, telephones or other improve- 
ments. The original cost of these may be considered a capital 
expenditure. 

94. Expenses, or Temporary Outlay in Forestry. — Temporary 
or current expenses would ordinarily include raw materials as 
well as items like wages (§21). But when wages are expended 
on planting trees and when the raw material consists of stand- 
ing timber, which will remain as property for a period of years, 
this treatment is open to question. After the forest property 
has passed through its initial stage of construction, and is pro- 
ducing annual revenue, many items, such as reforestation, which 
at first call for an initial investment, can be regarded as current 
outlay. In this class will fall all expenses for upkeep of im- 
provements. 

95. Land. — Land is the one investment which can be credited 
as capital not ordinarily subject to depreciation, and indispen- 
sable to forestry. It remains after the timber is harvested. 
The purchase price of land is the only land value which can 
legitimately be entered in the cost account, and this valuation 
can remain the same as long as the owner retains the land for 
forest production. A sale of the property, terminating the 



72 FOREST VALUATION 

ownership and cost account, calls for a revaluation of land (§§ 6i 
and 62). 

Bare land suitable only for forest crops does not command 
a high price (§ 96). 

96. Standing Timber. — By definition, real estate comprises 
land and all that stands thereon. A purchaser of land acquires 
all permanent improvements. These improvements may be 
sold separately, but always with the stipulation that they are 
to be removed within a given time. 

Standing timber is part of the real estate, and a purchase of 
land includes the timber, unless excepted by the owner subject 
to removal by him. Timber stumpage is sold by the owner on 
contract which allows the purchaser a definite time for removal, 
failing in which, the purchaser, in certain states,* loses his right 
to the timber. These timber rights sometimes run for periods 
of twenty years and while in force constitute a Hen on the 
property. 

By the time a crop of timber is large enough to cut, its value 
greatly exceeds that of the land. Virgin timber, containing ma- 
terial of high quality, shows a still greater excess of value (§ 184). 
In the past, lumbermen were quite indifferent to land values, 
regarding the title as desirable only because it made them inde- 
pendent of restrictions as to time and rate of cutting. What 
they purchased was the timber. Yet timber, whether young or 
old, is a "vanishing" asset. It must be converted eventually 
into income, and is subject to losses. Owing to the difficulty, 
in some cases, of distinguishing between the value of the land 
and of the timber, and the great preponderance of the latter 
value, the cost of standing timber is usually regarded as a cap- 
ital expenditure. Bonds may be issued, with this standing 
timber as security, provision being made to retire these bonds at 
a rate to more than keep pace with the cutting of the timber. 
Such bonds are in this sense paid out of "capital," as this "capi- 
tal" is converted into income. Bonds could not be floated on 
timber which was not about to be, or in process of being, cut. 

* This subject has caused extensive litigation, and has resulted in conflicting 
practice. State supreme court decisions must be ascertained in each locality. 



INVESTMENTS AND COSTS IN FOREST PRODUCTION 73 

97. Permanent Improvements and Equipment. — On any prop- 
erty managed exclusively for forest production, and of sufficient 
size to demand continuous care and administration, buildings 
must be provided for the permanent force, both officers and 
laborers, especially since these tracts are not often conveniently 
near towns. Special telephone construction is often required. 
These are legitimately classed as capital expenditures. Stables, 
draft animals and tools come in this category, but proper allow- 
ance for depreciation must be made. 

In cost accounts for individual stands, it is proper to dis- 
tribute these overhead charges over the entire territory which 
they cover, pro-rating them on a per acre basis. The initial 
cost for these items may be included with the cost of land and 
timber. The annual charge for upkeep, or its equivalent in 
depreciation, must be entered as a current annual expense on 
the same acreage basis. 

98. Roads and Transportation Systems. — Lack of perma- 
nent roads or other means of transportation is characteristic of 
American forest conditions. To yield a steady income, a forest 
must produce wood annually for market, which requires the 
transportation system to be in continual repair. 

In inaccessible regions, timber must exist in sufficiently large 
bodies to justify construction of a system of transportation for 
its removal. The cost of transportation contains two elements: 
first, cost of construction; second, cost of transport. Con- 
struction cost, no matter how cheapened, cannot be reduced 
below a certain limit. Cost of transport is lessened by improv- 
ing the means of transportation. When railroads, roads or 
flumes are built for merely temporary use, the entire cost of 
construction, as well as transport, falls on the timber removed 
at the time, and is pro-rated for each unit of product as, for 
instance, per thousand feet of lumber. 

Since transportation is a feature belonging strictly to logging, 
it affects forest production through its influence on the value of 
stumpage. It is the universal practice in America to allow the 
cost of construction, as well as transport, to fall upon the logger, 
who takes it out of the price of stumpage. 



74 FOREST VALUATION 

In permanent forest property, this construction cost may be 
assumed by the forest owner, whether or not he intends to do the 
logging. This is necessary in order to permit of the radical 
change in logging from the removal of practically the entire 
crop at one time to the system of continuous removal of smaller 
quantities over the entire area. Under the latter system, no 
logging contractor could afford to construct his own transpor- 
tation facilities. 

Such permanent systems are a capital expenditure similar 
in character to land, and the overhead costs thus incurred 
should be pro-rated by area and charged as an addition to the 
cost of acquiring the property. The maintenance of transpor- 
tation systems is an annual expense to be pro-rated in the same 
way. The owner's benefit from thus assuming costs belonging 
to logging is obtained by appropriating a larger share of the 
general profits through increased value of stumpage. 

99. Silvicultural Operations. — All labor expended directly 
upon the forest crop constitutes a charge against the particular 
area or stand which is benefited. Such costs include planting, 
with the cost of the plants; weeding or removal of injurious 
"weed" trees or brush when the plantation is young; protection 
from insects by measures requiring expenditure of labor on the 
area; and thinning, provided this is done at a cost exceeding 
the value of the product obtained. Costs incurred in natural 
reproduction, by leaving a portion of the stand to serve as seed 
trees, correspond to the cost of planting and should be charged 
against the new crop. Practically all silvicultural expenses 
occur as single or initial costs, and not as annual expenses, when 
reckoned in cost accounts for the stand. In a forest under 
perfect management, costs of most of these operations consti- 
tute a nearly constant annual expense for the forest as a whole, 
and would so appear in the proprietary account. 

100. Protection Expenses. — Initial expenses for protection 
from fire take the form of measures for disposal of slash left from 
logging. This expense is chargeable to the cost of the new 
crop and may be so treated in a cost account. But in practice, 
where the owner is not doing his own logging, as in the United 



INVESTMENTS AND COSTS IN FOREST PRODUCTION 75 

States Forest Service operations, this cost is transferred wholly 
or in part to the logger, and taken out of the price of stumpage. 
By this means, the true nature of the expense is concealed. 
The loss in stumpage value is a present cost or investment in the 
new crop as surely as if the owner received full value for the tim- 
ber and re-expended the amount required for brush burning. 
This initial cost, then, accumulates interest until the new crop 
is cut (§ 107). For this reason, it has been advocated as an 
alternative, that a sum representing merely the annual interest 
on this initial expense could be expended annually on the area 
to secure better protection from fire, without increasing the 
total outlay. 

Fire lines will frequently be necessary, particularly where a 
bad hazard occurs and where an investment has been made in 
plantations. This constitutes a capital expenditure, especially 
where the initial cost of the lines greatly exceeds their subse- 
quent cost of maintenance. The charge must be pro-rated 
over the area benefited, dated from the year it was incurred. 
Subsequent maintenance of these lines, a necessity often lost 
sight of, is an annual charge per acre. 

Lookout towers and installation of telephones used in fire 
protection are of the same class of expenditure as fire lines. 

The labor employed in fire protection for patrol constitutes 
an annual charge. 

Extra costs of extinguishing fire, if borne by the owners, con- 
stitute losses, entered against the area burned, and recoverable 
in some cases as damages. 

101. Administrative Expenses. — With a large area and 
well-developed system of forest production, the administration 
of the tract involves not only all business matters dealing with 
sale of products, taxes, protection and silviculture, but includes 
as well the proper technical direction of the work to assure 
the success of the measures for forest production which are 
the basis of the business. The salary of a technical forester is, 
therefore, a necessity, and this must be pro-rated on an area 
basis. Should the tract be too small to justify such expense, 
the owner must seek occasional technical advice and trust the 



76 FOREST VALUATION 

management to a foreman who can follow directions. Such 
advice is best obtained, for very small areas, through the State 
forester. For larger areas it is practicable for several owners 
to co-operate and employ a forester. 

102. Taxes and Insurance. — Taxes are separately discussed 
in Chapter X. Under present systems of taxation they tend to 
increase and this, coupled with the uncertainty as to the amount 
and time of these increases, makes it difficult to predict the total 
cost of this item or prescribe the exact method of calculating 
it. In this chapter, taxes will be assumed as a fixed annual 
expense, to be added to that for administration and protection. 

Insurance is not as yet available in this country on growing or 
standing timber. The owner bears his own risk and losses. 

103. Interest Charges. — These do not appear in proprietary 
accounts except when money is borrowed (§91). In cost ac- 
counts, past interest may at any time be calculated at whatever 
rate is considered equitable. Since the periods intervening be- 
tween outlay and income may extend to over 100 years, the 
interest charges will often be found to far exceed the sum of all 
actual expenditures. 

104. Classification of Costs in Forest Production. — Follow- 
ing the suggestions in the above analysis of costs, the invest- 
ments in forest production may be grouped, for computation, 
into three classes: 

Group A . 

Capital expenditures for 
Land. 

Permanent improvements and equipment. 
Permanent roads and firelines. 

Group B. 

Crop expenses for 

Standing timber, which is often included with cost of land. 

Planting or cost of regeneration. 

Brush disposal or initial fire protection. 

Weeding. 

Protective operations. 

Thinning. 



INVESTMENTS AND COSTS IN FOREST PRODUCTION 77 

Group C. 
Annual or current expenses for 
Protection. 
Administration. 
Taxes. 
Maintenance of permanent improvements. 

105. Calculation of Total or Final Costs. — To compute the 
total final cost, with interest included, at the end of a given 
period, the items under each of these three classes may be 
totalled. 

The "cost" of each is the amount which should be charged 
against the resulting income, which in forestry is the stumpage 
value of the timber plus the revenue from other sources. 

In Group] A, the original capital, if maintained properly, re- 
mains intact at the end, and only the interest can be charged as 
an expense to the crop. Let Sc = cost of soil and permanent 
improvements. Then total cost is 

SAi-op-) -S.. (§87, Illb) 

In Group B, only those crop expenses which occur in the same 
year may be computed as one total. These expenses must 
eventually be met entirely from income and do not constitute 
capital expenditures. With the cutting of the timber, no por- 
tion of the remaining assets are available from which to return 
these costs. 

The total cost of all such items is found by Formula I in which 
C = initial investment, 
C (i.o/>") = cost at end of period. 

Expenses incurred in year d will cost 

Let Co, Cd, Ce, Cf = Initial expenses incurred in the beginning 
and in the years d, e and /. The sum of these costs is 

Co (i.or) + Cd {i.op--') -F C« {i.op^-^) + Cj (i.o/>"-0. 

In Group C, all annual expenses are totalled. The sum of this 
expense with interest is found by Formula Illb (§ 87). 

Substitute e for r to represent annual expense. 



78 FOREST VALUATION 

€ 

Then = R = E, capitalized annual expense. 

The sum of these expenses, provided they remain at a constant 
annual amount, is 

E (i.o/>") - E = E {i.op" - i). 

The analogy of this calculation to that used in Group A is 
evident. The difference is that in A, Sc represents existing 
capital which remains as an asset, while in C, £ represents 
a fictitious capital which may have no existence and is never 
expended. It represents the capital which would be tied up, 
in order to produce an income to just balance the expense e. 
This capital might, if the owner desired, be actually deposited 
at interest, when the expense e would be permanently taken 
care of and the capital remain intact at the end as in Group A. 
But the proprietor usually meets this expense out of income 
from other sources. The capital represented by E is, therefore, 

merely a mathematical device, and the expression better 

expresses the status of the item, as it emphasizes the annual 
expense. 
Should expenses increase, the modified Formula Ilia is used, 

by substituting £' for (§ 79) • 

o.op 

The total actual cost of production for timber grown under 

management covers the period from its origin to its removal. 

Adding the summaries for the three groups, we have 

G, = C (i.op^) + S, {i.op" - i) + £ {i.op- - i) 

= (C + 5, + £) i.or - (5, + E). (A) 

This formula suffices when all initial crop expenses occur in 
the first year. 

Income during this period serves to cancel an equal value of 
accumulated costs in the year in which it is received. Annual 
income usually serves merely to reduce the net annual cost, and, 
therefore, does not appear in the formula. But income received 
from the sale of produc.ts obtained from advance cutting, or 
thinnings, bears no constant relation to the total expenses for 



INVESTMENTS AND COSTS IN FOREST PRODUCTION 79 

the year. All income is equivalent to negative costs, and in 
this case the item is best carried with interest to the final 
year, when its total may be subtracted (§77). Otherwise a 
separate balance would be required for the year of receipt of 
this income, which would serve no useful purpose. 

Let Tp, Tg, Tr. = value of thinnings or other incidental rev- 
enue received at p, q and r years. The future value, at end of 
period, will be 

Tp (i.op'^-p) + T, {i.op"-") + r, (i.op"-^). 

Subtracting this income from total cost, including Q, Cg and 
Cf, we have the net cost of the growing stock, Gc. 
G, = (C + 5, + E) i.op- + Ca (i.o^-^) 

+ C„ (i.o/>"-0 + Q (i.o/>«-0 - Tp (i.op--^) 

- T, (i.o/>"-«) - r, (Lor-O - (5, + E). (Ai) 

There is no way of avoiding these separate calculations for 
single sums occurring in odd years. As each item is independent 
of the others, the apparent complexity of these formulae need 
not be a source of confusion. 

To obtain the cost of a forest, including both soil and timber, 
the cost of soil is not subtracted. 
Let Fc = cost of forest. 

Then Fc = (C + Sc + E) i.op" - E, 

and for the year a, 

"Fc = (C + 5o 4- £) I. or - E. (A2) 

106. Total Cost of Investments in Standing Timber. — Only 
a few instances are found in America where forest crops have 
been brought from seed to maturity under management, and 
it is still less frequently that actual total costs of production 
have been recorded. Practically all past transactions in land, 
for forest purposes, dealt with property which already contained 
standing timber. 

Cost accounts for such property begin with the purchase price 
and carry all subsequent 7tet expenses to the present, to final 
sale of the property, or to the year when the timber is sold. 
Since such property is purchased in a partially or fully developed 



8o FOREST VALUATION 

condition, with respect to the timber crop, and may include cer- 
tain permanent improvements, the cost to the purchaser may not 
coincide with the cost of production, for the sale is usually the 
means of realizing profit on the part of the original owner (§ 90) . 
This initial cost is usually a lump sum, which includes the value 
not only of all separate stands of timber, but does not often 
separate the value of the land from that of the timber crop. An 
analysis of this cost must precede any attempt to institute a 
cost-keeping system separately for different parcels or stands. 

Separation of the cost of land and timber, while usually 
postponed in such instances until actual separation occurs 
through cutting, is necessary if the true cost of holding the timber 
is to be computed, and the land permanently devoted to for- 
estry. But if the purchase is a timber speculation, and the 
land, after the timber is stripped from it, is to be sold or aban- 
doned, there will be no need of this distinction. 

In the former case, 

C-\-Sc= cost of timber and land, or purchase price of property. 

The purchase price of the property is substituted for cost of 
land plus silvicultural operations, in Formula A. The net cost 
of production for timber depends now upon the value agreed 
upon for the land at time of purchase, for this must be subtracted 
as representing a capital investment. The formula is in all re- 
spects identical with A, and interest accumulates for the period 
elapsing between date of purchase and date of final sale or in- 
come, which is assumed as n in the problem. 

When interest is thus computed as a cost on the investment 
in stumpage, as well as on taxes and other expenses, a rate of 
6 per cent will cause this "cost" to double in twelve years. 
The stumpage value must double in a shorter period or there 
will be no income to replace current expenses. This raises the 
important question as to the length of time which it is possible 
for private owners to hold stumpage without cutting it (§181). 
For periods of forty years or over, it might easily be shown that 
the costs of raising a new crop of timber leave a higher margin 
of profit than those incurred in carrying a mature crop with a 
high initial value, for the same length of time. 



INVESTMENTS AND COSTS IN FOREST PRODUCTION 8 1 

107. Costs of Forestry Compared with Destructive Lum- 
bering. — Owners of timberlands have the choice of two Hnes 
of policy. They may desire to retain the lands only until the 
timber is removed, when every effort will be made to sell or 
dispose of them. Or they may plan to hold these lands indefi- 
nitely, with the intention of producing or securing a new growth 
of trees. The former policy is usually accompanied by destruc- 
tive lumbering, so termed because the purpose of the operation 
is to remove every tree of merchantable value, at the same time 
undertaking no measures to reproduce or perpetuate the forest. 

The financial distinction between these two policies lies in 
the character of the investment required for forestry. Destruc- 
tive lumbering squeezes the last cent of capital from the forest, 
wrecking it as a productive enterprise, and converting it into 
money profits. In this process, the cost of transportation is 
reduced to a minimum by use of temporary structures and com- 
plete removal of the timber, by elimination of all care in felKng 
and skidding needed in preventing injury to young timber, and 
by neglect of the fire trap caused by the slash, and abandonment 
of the land to promiscuous broadcast burning. Under such 
conditions, stumpage brings its highest prices and the profits to 
logger and owner are greatest in amount. But there they cease. 

In any other form of business, similar results may be obtained 
should the owner close out the enterprise by the sale, not only 
of the net product, but of his reserve stock, fixtures and capital 
assets. The profits obtained on stumpage under destructive 
lumbering are higher than the business of forest production 
can earn or is entitled to, and the entire structure of lumbering 
as it is carried on to-day will crumble away with the exhaustion 
of the raw materials, having converted the chief asset, produc- 
tiveness of forest lands, into money. 

The investment which forestry may require, and which de- 
structive lumbering avoids, consists of 

Additional cost of transportation in logging. 

Additional felling and skidding costs. 

Brush disposal. 

Cost of seed trees. 



82 FOREST VALUATION 

With the entire cost of building roads charged against the 
logging, and pro-rated over the amount of timber logged, any 
reduction in this quantity, especially if the area is not corre- 
spondingly reduced, increases the unit cost of logging by nearly 
the same ratio. It is not often possible to cheapen the means 
of transportation to conform to the lessened cut (§ 98) . 

Felling and skidding will cost more in proportion to the care 
needed in avoiding damage to young timber. 

Brush disposal (§ 100) is almost always needed. It frequently 
happens that as a result of this measure, the costs of skidding 
are correspondingly reduced. 

A question may well be raised as to whether the sum of these 
extra expenses constitutes a loss of profits on the crop being cut 
or a diversion of profits into initial investments on the next 
crop. Should the total extra cost, thus incurred, be charged as 
initial cost or silvicultural expenses, to accumulate at compound 
interest, it would constitute a heavy burden on the succeeding 
crop. Viewed from the standpoint of destructive lumbering, 
this cost, taken from profits, is a deliberate reduction of ordinary 
profits and must be charged against future income. But from 
the standpoint of forest production, this excess profit is not a 
true profit at all, but the wrecking value of the "plant" added 
to legitimate profit. Nomial profit is that which will leave the 
productive capital intact. From this standpoint these "extra" 
costs of logging would be considered as "ordinary" costs, falling 
on the logging and cancelled by income from sale of logs, and 
would not be regarded as an additional investment in the new 
crop. These two opposing tendencies are best illustrated by 
the expense of burning brush (§ 100). 

The investment represented by the stand of timber left after 
logging is more easily classified. Should this consist merely of 
seed trees, it can be regarded as a loss only in case these trees 
will not live until the harvesting of the next crop. If they 
survive, they represent an investment from which the returns 
will be: 

The future value of the trees themselves; 

The value of the new crop. 



INVESTMENTS AND COSTS IN FOREST PRODUCTION 83 

This investment feature is even more conspicuous in the case 
of stands in which a large per cent remains after logging. 

In either case, the sale of the greater portion of the merchant- 
able stand gives the basis for an appraisal of the remaining timber. 
A balance may be struck between past costs and income and 
the remaining crop credited with its present value, which is 
then charged as an initial investment for the ensuing period. 
This would show profits on the entire crop, and a reinvestment 
of the portion left standing. If this appraisal is not used, the 
profits are confined to the timber actually cut, and the invest- 
ment would not be charged against the new crop or period. 

The former method of accounting is preferable. The use of 
profits to cancel investment may be pushed to illegitimate 
lengths, as when income from the sale of timber is allowed to 
" wipe out" the cost of the land, which is then carried as having 
no "cost" or "value" for a succeeding period. In this case, 
income from sales should be permitted to offset only the cost 
of the timber sold, while the land (§ 96) must be separately 
valued, and will be charged with interest in the future reckoning. 

108. Cost of Many-aged Forests. — Proprietary accounts of 
investment for large forest properties are kept very simply (§91). 
The same is true of such an account when dealing with single 
stands composed of trees of many ages. But the question 
arises as to whether income from such a stand should cancel 
original capital investments, or be regarded purely as interest 
or dividends on this capital. 

If the forest is established and is renewed, so that, whether 
the cutting be annual or at intermittent periods, it may be 
maintained in amount and value indefinitely, the cost of the 
stand can be considered as a unit, regardless of the separate 
age classes (§ 161). This cost may be the price of purchase or 
the cost of production (§ 109). In a stand of all ages, producing 
annual income, this cost does not increase and the net income is 
merely the annual dividends on the investment. None of this 
income is needed for the replacement of capital. 

In a forest yielding an intermittent rental, the cost or total 
investment continues to increase (§ 92) until a payment of 



84 FOREST VALUATION 

income is received. This payment must be regarded as can- 
celling the additional capital invested since the last payment. 

Where yields are irregular in time and value, and yet there 
always remains a considerable stand of timber on the ground, 
the relation between cost and income becomes a matter of judg- 
ment or adjustment. The object should be to insure the return 
of the capital invested in the timber which is removed, and carry 
as a cost or further investment only a reasonable balance of 
original cost against future income. The cost of a forest is the 
sum of the net costs of the separate stands or parcels. 

109. Cost of Producing a Normal Forest. — A normal forest 
is one from which an annual income may be obtained without 
diminishing the amount and value of the capital or assets. This 
requires the presence of equal productive areas in each age class. 

Granting that the cost of each parcel of land is charged to 
this forest in the year in which the crop upon it is started, and 
that it takes n years to establish the forest, an area equal to 

- of the whole must be reproduced each year. The total annual 
n 

expense e applies to the entire area of the forest. C is required 

to plant the parcel. The capital tied up in the investment 

for the year will then be C -f 5^ + £ (§ 105). 

Since an equal area and capital investment is added each year, 
on which interest accumulates till the year n, the sum of costs 
forms a series, with {C -\- Sc -\- E) as the first term and i.op 
as the ratio of increase. See Formula III. 

The sum of these costs is 

{C + S, + E){i.op^-i) ^ 
o.op 

But the capital E is fictitious (§ 104) and this has been intro- 
duced n times. In the same way, Sc may be deducted as a 
capital asset, totalling nSc. 

This makes the net cost of production for the timber alone as 

G, = iC + S. + E)U.op'-.) ^ 
O.op 



CHAPTER VII 
THE VALUATION OF FORESTS 

110. Valuation Accounts in Forestry. — Just as the proprie- 
tary and cost accounts in forestry (Chapter VI) deal with the 
personal investments of the owner and past elements of cost 
and income, so the valuation accounts in forestry deal entirely 
with material assets (§ 54) and determine their value. The 
basis of this determination is the forest inventory (§ 55) which 
shows the area of land of different qualities, the amount and 
kind of timber and of other resources, and any other property 
included in the forest. 

111. Income as the Basis of Value of Forests. — This phys- 
ical property must be valued or appraised (§§ 18, 60). Follow- 
ing the conservative systems of accountants, the values entered 
for land, timber, buildings or other forms of property cannot 
exceed what was actually paid for them (§ 56). Such an asser- 
tion does not mean that the actual value of the property remains 
at cost, but that growth in value is not considered equivalent 
to realized income. An increase in value of assets may and 
does occur, and, with growing timber, is the rule; but the ac- 
countant in all such cases desires to await the actual sale of the 
product, and credits this increase in value only when received 
in the form of money returns. 

While this custom protects the proprietor or stockholder, no 
pretense is made that the book values, based on cost, represent 
the actual value of the property. In Chapter IV the basis of 
value is seen to be future income (§§ 61 and 62) and the true 
value of all assets is derived from this income, discounted to 
the present, minus future costs. 

In order to grasp the principles employed in appraising for- 
est values, the relations between physical assets, income and 
value must again be emphasized. First, the forest land, with 

85 



86 FOREST VALUATION 

its growth or stand of timber, is the property to be valued. 
Second, this land, by producing timber, and the timber, by grow- 
ing, yields saleable products whose final sale produces income. 
Third, the income, expressed in money, has an appraised value. 
As the final step, the value of the income is discounted to deter- 
mine the value of the physical capital which will produce it. 

This process cannot be short-circuited. The sale value of 
forest land or timber does not represent any quahty inherent 
in the land or timber except the capacity to produce income, 
and the value of the property must first be based on the valua- 
tion of the income. 

The income from forests is principally the value of timber 
sold on the stump, or the proportion of profits from logging 
which is due to the owner of stumpage. Secondary income is 
obtained from thinnings or advance cuttings, and from pastur- 
age, or hunting and fishing rights. Other sources of income are 
by-products, such as naval stores, or tree seeds, nuts, bark, 
sugar, shrubs, herbs and fitter. 

The present value of the forest is the sum of the present or 
discounted values of all items of income expected in the future, 
less the present value of all items of anticipated expense (§62). 

Sale value bears the same relation to capital or expectation 
value for forests as for any other form of property (§ 59). But 
since sale values are the expression of average general opinion, 
the sale value of forest land and young timber will be apt to 
depart widely from the capital or expectation value of such 
property in regions where the business of forest production is 
not recognized, and lands are abandoned after logging or de- 
voted to agriculture and grazing. 

112. Value of Forest Property for Destructive Lumbering. — 
When the owner intends to remove the timber and devote the 
land to other uses, his income will consist of: 

Yield of timber; 

Value of land for other purposes after timber is removed. 

As long as the timber remains, the land cannot be utilized 
fully for anything but the timber crop. Grazing is only a sec- 
ondary source of revenue. When cleared, its value is considered 



THE VALUATION OF FORESTS 87 

as depending solely on the net future income from other uses, 
such as agriculture or grazing. Since these are enterprises not 
directly connected with forestry, it may be technically assumed 
that the forest owner sells the land, and the sale value received 
completes his income and terminates the enterprise. 

The total present value of forest property based on the 
income from destructive lumbering is determined as follows: 

F^ = sale value of forest property, including both land and 

timber. 
Y = yield or net stumpage value of timber in final cutting. 
Tp, Tg, Tr = yield or value of thinnings or timber removed 

before final cutting. 
Ss = sale value of land when finally cleared of standing timber. 
e = annual expenses. 
E = capital value of annual expenses. 
a = present year, or the year a dating from the origin of the 

stand. 
n = year in which final cutting is made, dating from the origin 

of the stand. 

The period of discount will then hen — a years. 

In the year of sale, and previous to its consummation, a and 
n coincide. The value of the property for immediate sale is 
then 

F, = Y-\- S,. (B) 

When the year of valuation a precedes n, the value is as 
follows : 

Value of Y for year a 

= — ^ (see II). 

Value of Tp, T^, Tr for year a 

T T T 

J. P J. g J. f 



i.op^-" I. op"-" I. op'' 
Value of Sa for year a 

= -A_. 

i.o/>"-" 



88 FOREST VALUATION 

Cost oi eiorn — a years = (see Illb, II), which 

i.o^"~" 

becomes E 



I. op"-" 
Omitting the item of thinnings, 



ap _ F + >S. -£(i.o/>"-°-i) 



I. op"-" 



I.O/)"~" 



- E. (BO 



Including thinnings whose income is expected in the future, or 
between the years a and n, 

af _ ^ ~r ^g ~r -^ p -l. ^ I -^ <? |_ -^ r 



I. op"-" I. op"-" i.op"-" i.op'-" 

_ Y-\-S, + E + T, ii.op''-") + T., (i.op"-") + Tr ji.op"-'-) ^ 

I. op"-" 

(B.) 

113. Value of Forest Property for Continuous Forest Pro- 
duction. — The substitution of sale value of land for its value 
determined from income was a makeshift justified by the 
change in its use. True forest land, devoted permanently to 
producing timber, must be valued on the basis of the sum of all 
future income which it is capable of producing. This will in- 
clude the net value, not merely of the present stand, but of a 
succession of timber crops, extending to infinity (§ 86). 

The relative present vallie of the first crop compared with 
others to follow is very large, but merely because the interval 
between payments is correspondingly long. The income from 
sale of a crop of timber does not differ in character from the 
monthly payment of rent, and the value of the forest is as truly 
the sum of all present values from future crops as that of the 
house is the capitalized net rental or income. In the same way 
that the value of the house represents, not the gross rent, but 
the rent minus all outlay such as taxes, repairs and depreciation, 
so from all future income from timber, deductions for expenses 
must be made to get total net value. 



THE VALUATION OF FORESTS 89 

114. Value of a Forest of Even Age Just Previous to Cutting. — 
A forest or stand of even age may be cut clear at one time and 
replanted. During the period immediately following the cut- 
ting, the soil is bare of trees, while at all other times it is occupied 
by timber of constantly increasing size. 

Since every item of either income or expense must be assumed 
to recur for each future timber crop, the total present or dis- 
counted value for each item is found by Formulae IX to XII. 

For the year n, and just previous to receipt of income Y , the 
value of income Y, being the sum of all future payments dis- 
counted to the present year, is 

Y Y Y 

\ L . . . J L_ 

I. op" LOp^"" I.Op^ ■ I. Op" 

The cost of planting or reproduction, which in destructive 
lumbering does not occur, falls here in the same year as Y and 
recurs every n years. 

Value of expense C, totalled in the same manner, is 

c + -^ + -^+ • • • +-^ = C+ ^ 



I^+7T7; + 7T7^+ • • • +7TI^=^ + ,_:. , (§85,XIa). 



i.op" i.op'^" i.op^ I.O/>"- I 

The annual expenses e recur at intervals of i year, by defini- 
tion, and are computed from the end of each year. 
Value of the sum of annual expenses e: 



l.Op l.Op^ LOp"^ I. Op"" I. Op— I O.Op 

Let F^ = expectation or capital value of forest property for 
continuous production. 
Then 

F, = F + - ^ ■ -(c-\- ]-E 

i.o/>" - I V i.o/>" - I / 

= Y+ ^-^ -(C + E), (C) 

I. op" — I 

which is the value of forest property just previous to removal 
of the timber. 

In this formula, no account has been taken of other items of 



90 FOREST VALUATION 

expense corresponding to C but falling at different years, nor 
of income from thinnings corresponding to Y but received 
previous to this final cut. 

The present value of these items is found by Formula X, since 
each single payment, while not repeated during the rotation, is 
assumed to recur in the next rotation, and the total of all future 
payments forms the series. 

Let Tp = income from thinning in year p, recurring every n 
years forever. 

T 
Then — ^— is the value of Tp in the first year, n. 
I. op'' 

The series is 

-^ p I -^ p I -^ p 4_ , . . _|_ P . 

l.OpP I.OpP-^" I.O/>P+2r. ' I.O/>*' 

The sum is (Formula Q4) 

Tp 
i.op^ _ Tp (i.o^"-p) 
I i.o/?" — I 

I.O^" 

By substituting q, or r, for p, the present capital value of 
other items of income or of expense, for any year, is obtained. 

The present value of forest property just previous to removal 
of a final cut of timber is summed up as 

Y + Tp{i.op^-^)-\-T,{i.op--<^) 
+ Tr {i.op^-') - C - Q {i.op--') 
-C(i.o/>"-)-C,(i.o/>"-0 (Ci) 



F, = F - (C + £) + 



i.o/>"- 



115. Value of an Even-aged Forest for Any Year. — The value 
of the forest for any other year, or during its growth, is ob- 
tained by discounting the above value for the period previous 
to this final cut. The forest has its maximum value just before 
the principal yield is removed. The further into the future this 
income is postponed, the less becomes the present value of the 
property. 



THE VALUATION OF FORESTS 9 1 

Should the value be sought for the year a, and this year be 
but one year previous to the cut, the value of the forest is dis- 
counted n — a, or one, year. As a is dated earlier and earlier 
in the hfe of the stand, the discount period n— a increases, until 
when a = o, just after the felling of the old crop and previous to 
the starting of the new one, we get the smallest value to which 
the property shrinks in the entire rotation. 

With the advance of the date of calculation to the year a, 
both the future yield Y and the cost of planting C occur first 
mn — a years. The annual expenses, since they are calculated 
for the same interval, and extend to infinity in both cases, have 
the same capital value E. 

By Formula Xa, the value of the forest is 

ap^ ^ Y (i-o/^°) _ Cii.op") _ ^ 
I. op" — I i.op"- — I 

^ (Y-C) ..op- _ ^ 
I.op" — I 

Items of either income or expense occurring at other than n 
years will fall either previous to or subsequent to year a. Those 
preceding a are not considered in the value of the standing crop 
(§ 68), but their occurrence in the subsequent rotations affects 
the value of the forest. 

A thinning occurring in the year r subsequent to a has a value 

T 

at present (year a) of ^ — 

^ ^ ^ I.op'-" 

The sum of future values (Q4) is 

I.op'-" _ r,(i.o/>''+°~'-) 

I I.O^" — I 

I.O/>" 

A thinning occurring in the year p previous to a-2 has a present 

T 

value (year a) of r 



92 FOREST VALUATION 

The sum of future values (Q4) is 
T 

J- r> 



I I. op"— I 

I ■ ^ 

I.O^" 

These expressions are equally applicable to costs occurring 
before or after the year a. The present value, in year a, of an 
even-aged forest or stand, is summed up as 

■ Y (i.o/)«) + Tp (i.op^-^) + T, {loP'^-") 
+ r, (i.o/»«+°-'-) - C (i.o/>«) - Ca {i.op--") 
- C, {i.op"-') - Cf {i.op"-^) 



ap 



i.op"- 



- E. 



This formula may be expressed in another form. 
ap _ 

V i.opp i.op" I. op'' i.op'^ i.op^ i.o/>V _„ 

I.O/>" — I 

(Di) 

The chronological relations of these items are set forth in 

Diagram II. The present year is the basis of valuation. Past 

occurrences are ignored. But in the terminology, the numerical 

value of a is reckoned from the past year o, or date of origin 

of the crop, which is also the basis for the other dates. 

The year 2a is just n years in the future. The Formula Di 

expresses the value of the items computed at compound interest 

to the year 2a, when the balance is struck which gives net 

value. This net income recurs at intervals of n years from 

/ 

date, and its present value is , hence the above result. 

' ^ i.op" - I 

116. Value of Forest Soil. — The value given in Formula C 

was for a forest just previous to removal of the final cut. This 

value steadily diminishes as the date of this cut is assumed to 

be further into the future until the lowest ebb is reached, just 

before the discount period overlaps the date of the previous cut. 

A similar fluctuation in value occurs in the case of an account 



THE VALUATION OF FORESTS 



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94 FOREST VALUATION 

in a savings bank from which the accumulated interest is with- 
drawn, say every lo years. For land which is bare of trees but 
in condition to be planted at once, the period intervening to 
reduce the value of this prospective income coincides with that 
for growth of the crop. But should the land first require drain- 
ing, or other preparation as in the case of peat lands or shifting 
sands, a still further shrinkage of prospective value occurs, be- 
cause of the lengthened time and extra expense intervening. 

This discounted value of future income, computed for a date 
just previous to the origin of an even-aged stand of timber, 
gives the value of forest land bare of trees. 

This value is obtained from Formula C, by omitting the value 
of the timber Y. Let S^ = expectation value of forest land. 

Then 5", = ^ ~ ^ - (C + E), (E) 

i.op"— I 

or 

jF + Tp (i.o^«-^) + r, {Lop'^-") + Tr (i.c^"-"-) 
5 _l -C-C,(i.or"'^)-C(i.o/>— )-C,(io/>"-0 .^ ^ ^s (El) 
i.o^" - I 

5„, the expectation or capital value of forest land bare of trees, 
may be likened to the value of bare land suitable for farm crops 
or orchards. In the case of farm land, it may happen that the 
sale value of one annual crop will equal or exceed the value of 
the land, and farms are usually sold subject to crop removal 
or in the winter. With orchards, the value of the bearing trees 
greatly enhances that of the bare soil. Even a young orchard 
increases land values. In the latter case, it is of small moment 
whether value is separated into the value of the land and that 
of the fruit trees, for both are sold together. With forest trees, 
the relation between land values and ultimate income is exactly 
the same, but the period covered by the growth of the stand is 
so long that one is apt to lose sight of the fact that this so- 
called value of land is merely the discounted value of the future 
crops of timber. 

This soil value S„ represents the value of all future income 
dating from a point just subsequent to the complete removal of 



THE VALUATION OF FORESTS 95 

a crop of timber. It is the value of all future crops exclusive 
of the one occupying the ground. 

But Sy represents this value correctly, only for the year of 
cutting, or just previous to planting. Dismissing the idea that 
Sy represents the actual "intrinsic" value of the soil itself, and 
regarding it solely as the discounted net value of the future re- 
ceipts from timber, it is seen that this value S^ holds good only 
for the one year. Just previous to the cut, the property is worth 
Y -\- Sy. Just subsequent to cutting, the value is 5„. But when 
this net income is discounted to any previous year a, its value 

ceases to be 5„ and becomes The value of the entire 

i.o^""" 

property, soil and timber, as determined from the net revenue 

(see § 112, Formulae Bi and B2), is the sum of the net income 

from the standing crop plus the discounted net income from 

future sources, represented by The value of the stand- 

ing timber is — (E — ) • 

^ I. op"-" V i.op"-V 

The sum is, therefore, 

^ Y + S^ + E _ ^ ^^^ 

I. op"-" ^ ' 

But since 5„ reappears every n years as the net value of bare 
soil, it may be assumed that this represents the value of the soil 
during the intervening period, and that the excess of value for 
the property represents the value of the trees or growing stock. 
Under this assumption, S^ might be regarded as the fixed capi- 
tal, corresponding to a sum of money, and the value of the 
timber as the accumulating interest earned by this capital. 

To determine what annual interest this soil capital is earning, 
it is necessary merely to multiply S^ by the rate of interest p 
used in calculating it. 

5„ X o.op = soil rent (§162). (E2) 

Expectation value of soil is merely an expression of net income. 
Instead of being permanent or fixed, it is a prediction or forecast, 
and changes constantly (as do all values) not only with every 



96 FOREST VALUATION 

change in economic conditions affecting the price of products, 
but with the opinions of property owners as to the amount and 
present value of the anticipated income. Since it is the furthest 
removed from actual income, soil value is the most unreliable of 
all forest values, and is subject to greater proportional fluctua- 
tions than values of standing timber. 

117. Value of Many-aged Forests Producing Regular In- 
come. — The true character of this capital value of bare forest 
soil is further emphasized in the valuation of stands of timber 
composed of trees of many different ages. 

Two cases may be presupposed. First, the existing age classes 
are so distributed that an amount of timber can be cut at 
equal intervals of time, and of approximately equal quantity 
and value. Second, the age classes are irregular in quantity 
and unevenly distributed as to age. This second example is 
the prevalent type of many-aged forest. 

In neither case is the land ever clear of timber, unless the young 
age classes are destroyed by fire or logging. It follows that for 
a forest of this character the value of bare land cannot be deter- 
mined, except by making an artificial assumption of an even- 
aged stand of equal total yield with that of the many-aged 
forest, and in which the trees take an equal time to develop. 
But the trees in the all-aged stand take longer to grow than 
they would if even-aged, on account of suppression or shading. 
The correct determination of soil value, apart from the stand, 
for such forests is therefore quite unsatisfactory. With a slow- 
growing species the values indicated for bare soil may be nega- 
tive and are usually very low. 

But the forest itself, or total property, both soil and timber, 
even after a cutting has just been made, has a positive and often 
a high value. 

Whether the interval between cuttings m is long or short, 
the value of the forest just after the cut is 

^"^ -(C-fE). (F) 



I. op""- I 
But in this case, the formula, although similar to that (E) for 



THE VALUATION OF FORESTS 97 

bare soil, differs in the period m and gives, not the value of soil, 
but of the soil and timber remaining after the cut. It is the 
value of the real estate or forest. 

The term F„ is thus used to indicate the value of the forest 
just following a cut. 

For any year previous to a cut, the value of the property may 
now be found by discounting the net value of this yield to the 
present, and adding the discounted value of F^. 

This gives 



I. op"''" i.op" 

Y + F„ + E ^ 



(Fi) 



I .op""'"- 
The value of a forest producing a regular annual income is 

found by capitalizing this net income, using Formula XII, . 

o.op 

The annual income will he Y + Tp + Tq -\- Tr. 

Annual expenses are C -\- n X e, since e is the annual expense 
for but one area or age class and there are n age classes in the 
forest. 

Other expenses, as Q, Cg and Q, also occur annually. 

J. Y + Tp + T, + Tr - (C + C, -\- C, -\- Cr -\- n X e) .„ . 

O.op 

The net income, which is thus capitalized to obtain value, is 
termed the forest rent (§ 162). 

118. Value of Many-aged Forests Producing Irregular In- 
come. — Should the value of irregular many-aged forests be 
sought, the period must first be determined, which is required 
by the average trees to become merchantable. The stand must 
then be roughly grouped into its age classes, and the approxi- 
mate per cent of total area agreed upon which each age class 
occupies. Each of these yields must then be discounted to the 
present, with a value determined by its area. To get the net 
value of each crop, the future expenses must be pro-rated ac- 
cording to the same distribution of area. Finally, the total value 



98 FOREST VALUATION 

is obtained if each yield is treated as a recurring rental (Formula 
X, Diagram II). An example of such a valuation would be: 

Crops cut J. 

in year a, ~ total area, 

X 

in year b, - total area, 

y 

in year c, - total area. 

z 

If total value of all crops is Y and total expense e is capital- 
ized as E, and there is no expense for reproduction, the value of 
the forest is: 

V Y Y 

- {i.op^-") H — {i.op''-^) + - (i.op^-') 

"F.=^ y- '- E. 

I. op" — I 

Should an expense for reproduction, C, occur at the time of 
cutting, or any other initial expense be incurred at that time, 
this expense is subtracted from Y in that year. 

As 

V — r V — r Y — c 

- — - (i.o/>»-«) + — - (i.o^«-*) +- — ^(i.or'O 

aF =-Ji y ^ E. 

i.o/^" - I 

(F3) 
Formulae are merely convenient methods of calculating re- 
sults after the facts are obtained. Any large area of forest 
requires careful analysis and separation into its component 
parts before any of the methods of computing value can be 
applied. 

119. Value of Timber Separate from Land. — When for any 
reason the value of the timber must be separated from the value 
of bare land, it may be done by subtracting this latter value 
Sv from the formulae giving the total value of the property. 
Formula D2 then becomes 

''G.-~'^^-{S.+E) (G) 



THE VALUATION OF FORESTS 99 

and Formula Fi reads 

°G.= ^ + ^:+^ -(5„+£), (GO 

i.op 

provided in this case that the value of the soil can be determined 
or agreed upon apart from that of the poles, saplings and seed- 
lings which increase the value of F^ over that of S^,. 

For a normal forest (§ 109) producing annual income, the ex- 
pectation value of the standing timber, separate from the land, 
may be found by subtracting n X S^ from Formula F2 which then 
reads 

Cjv = 7 n{\). (G2) 

.op 



CHAPTER VIII 
FOREST STATICS — THE BALANCE SHEET — PROFITS 

120. Determining the Profits of a Forest Investment. — Forest 
statics is defined by Schlich * as ''the science which weighs and 
considers the comparative merits of the different methods of 
treatment to which forests may be subjected. The financial re- 
sults, or income-yielding power of an undertaking, are expressed 
by the proportion existing between the yield and the capital 
which produces it." 

Two distinct methods are possible in preparing a financial 
statement in forestry (§ 73). The first may be termed the spe- 
cific balance sheet and conforms to the principles of accounting, 
by recording only the actual cash investments as credits, and 
valuing the assets preferably at actual cost. By means of the 
supplementary profit and loss account, the net income, or loss, 
is annually transferred to the balance sheet. 

This specific balance sheet does not reveal profits until they 
are actually realized. It is therefore extremely conservative. 
For a business based on deferred income as in forest production, 
the annual net deficit of expenses over income may continue for 
many years, requiring continuous increase in invested capital, 
which would be further increased by borrowing, and adding to 
expense the actual cost of interest on these borrowed funds. 
The balance sheet indicates an increasing deficit, up to the time 
the timber is cut. 

With the receipt of this income, the total assets are suddenly 
increased to several times the total investment, showing an ap- 
parent profit of hundreds of per cent in case of even-aged stands 
harvested after from 40 to 60 years. 

* " Manual of Forestry," Volume III, Forest Management, by Sir William 
Schlich, 4th Ed., Chapter VI, p. 149. Bradbury, Agnew Co., Ltd., 10 Bouverie 
St., London. 191 1. 



FOREST STATICS — BALANCE SHEET — PROFITS lOI 

Such results evidently do not fully accomplish one important 
purpose of a balance sheet, which is to reveal to the owner the 
true financial status of his investment. Two elements of eco- 
nomic importance have been neglected, which entirely alter this 
status. The expectation value, not the cost of the assets, is 
the true measure of the debit entries, while the profits finally 
credited are not revealed in their true relation to costs unless the 
time required to earn these profits is given proper weight in 
the balance by exhibiting the interest at p per cent which should 
have been earned on the invested capital during the period. 

A statement which includes these two factors, expectation 
value and interest on costs, may be termed the "economic fore- 
cast." Revaluation of assets to coincide with present value 
rather than cost is practiced in commercial accounting when 
circumstances seem to justify it (§73). But the addition of 
unearned interest as a cost is universally excluded in specific 
accounts. The economic forecast would include such interest 
on costs, for in no other way can the owner inform himself of 
the relative value of the profits derived from income, or whether 
there is any enterpriser's gain. The apparently enormous final 
profits shown by the specific balance sheet may, when tested by 
this economic comparison, be revealed as equivalent to less than 
p per cent, which is no profit at all as measured by the standard 
of enterpriser's gain (§42). 

In this economic statement the proprietary side ordinarily 
shown as credit is excluded altogether, and the costs are shifted 
to the right-hand column in order to compare them with actual 
value (§ 73), and reveal potential profit or loss. The statement 
formulated in this manner is thus purely impersonal, and does 
not distinguish between borrowed and personal capital. It is 
similar to that which would be formed by comparing a cost 
account for manufactured articles, as credit, with the sale value 
of the article as debit. But in the case of productive property, 
this comparison must be made far in advance of the receipt of 
final or total income and is a balancing of cost against expecta- 
tion value for the entire enterprise. 

That the economic statement will show entirely different 



I02 



FOREST VALUATION 



results from the specific balance sheet is evident. When the 
accountant insists on retaining land and timber in the balance 
sheet at their original cost, the credits will exceed the debits 
by the amount of annual expenses not entered as a capital ex- 
penditure. This deficit is further increased by interest paid 
on borrowed capital if such expense has been incurred. By 
contrast, the economic statement shows an even greater "cost," 
since interest is added as a cost item to all capital invested, 
whether borrowed or not. The assets, on the other hand, are 
treated without any regard for actual cost, their value being 
determined entirely on the basis of future income (Chapter VII). 
The value of forest property, which is used in the economic 
statement, is its expectation or capital value, until it reaches 
maturity, when the capital value of the standing timber is 
merged in the sale value from which it is derived. The com- 
parison for timber property at any year previous to maturity 
of the timber will show. 



Debits. 


Credits. 


Expectation value of 
property, consisting of 
Young timber, 
Forest soil. 
Indicated or potential 
loss. 


Cost of property, consisting of 

Interest on all items of cost. 
Indicated or potential profits. 



The economic forecast in forestry thus consists of balancing 
past costs, with compound interest to date, against future 
income (§ 62) discounted to date, as represented by expectation 
value of assets. By thus comparing the relative values of past 
net outlay and future net income, for any year a, the exact 
economic status is revealed for that date. 

This method of valuation for forest assets may be compared to 
the appraisal of the property and business of a lumber company 
for purpose of sale. Cost would not finally determine the value 
placed upon any item of such property. The mill and logging 
road, machinery and stock, would be valued on the basis of 
their future usefulness to the purchaser and present owner. 
The timber would be appraised at going prices for equally 



FOREST STATICS — BALANCE SHEET — PROFITS 103 

good stumpage. Should the sale be consummated these ap- 
praised values are reahzed, and the profit shown in this tenta- 
tive or economic statement becomes an actual profit, entered 
specifically on the books. 

To what extent the value of assets in a specific balance sheet 
should be increased above cost of purchase, is a question to be 
determined by the character of the business. Unless these 
increased values are eventually reahzed, the profit shown by 
reason of such increase exists merely in anticipation, and until 
it is secured, this profit cannot be distributed as dividends. 

There is considerable difference between the financial status 
of a lumber company conducting an extensive operation with 
stumpage held merely as a timber mine to furnish wood until 
exhausted, and that of a forest owner engaged in growing timber 
as a business. The former concern is obliged to adhere rigidly 
to the accounting principles commonly accepted in business 
circles. Its timber will be entered at cost, unless a bond issue 
is floated, when it is customary to appraise the timber at its 
present stumpage value and to make a far more complete esti- 
mate of its amount. Bonds are secured by value, not by cost 
of property bonded. The interest on these bonds must be met 
annually or foreclosure follows. Taxes, protection and interest 
are, therefore, formidable items of expense and timber must be 
cut each year to produce sufficient income to cancel these costs 
for the entire remaining body of stumpage. 

But because of these conditions, the actual status of the 
lumberman's investment tends to follow a similar course to 
that of an investment in growing timber. The first years will 
tax all the resources of the owners to keep ahead of their obH- 
gations. Need for income is urgent. The tendency is to 
greatly increase the size and capacity of mills and operations. 
This universal tendency causes overproduction of lumber and 
defeats its own ends by lowering prices. 

But once a concern has weathered this initial period, and 
reduced its indebtedness and carrying charges, the final years 
of the operation become more and more profitable. It follows 
that those operators who have the greatest amount of capital 



I04 FOREST VALUATION 

behind them, and who do the least borrowing and maintain 
operations in a region after others have ceased, reap large profits, 
while the small investors, or firms attempting too much with 
limited capital, are often bankrupted in the first stage of the 
business. 

The investor must, therefore, distinguish sharply between the 
commercial or specific trial balance, and the economic forecast 
which accounts for time, includes interest on the investment as 
a cost, and bases the value of assets not on cost but on income, 
by the process of discount. Such a " balance " informs the owner 
of his true economic status, thus enabling him to determine his 
future policy — whether to sell, purchase or continue to operate. 
Economic, and not specific, profits are discussed in this chapter. 

121. The Rate of Interest in its Relation to Profits. — In 
securing an accurate statement or balance between past costs 
and future income or capital value, the effect of the element of 
time upon such relative values must be eliminated or equal- 
ized (§ ii). This is done by employing the same rate of inter- 
est (§ 38), p per cent, on both sides of the equation. 

The total amount of compound interest is increased by em- 
ploying a higher rate, while the same increase in the rate has 
the opposite eft'ect of lowering the present or discounted value 
of assets. This effect is due in each case to increasing the 
difference in value caused by the element of time. It follows 
that an increase in the standard rate of interest, p per cent, 
tends to obliterate the margin of profit on the credit side of the 
balance, and replace it with a debit deficit or loss. In other 
words, if the investor is satisfied with 3 per cent, and that rate 
is used in computing values for the balance sheet, the statement 
might indicate a profit, but if he uses 6 per cent as the necessary 
basis of comparison with other investments, the resulting bal- 
ance may indicate a loss, although the cash income and expenses 
remain the same in either case. The change is wrought wholly 
in discount or expectation value and in the accumulated ''cost " 
of compound interest. 

A rate of interest may be found for any given total of expense, 
on the one hand, and of income, on the other, which will just bal- 



FOREST STATICS — BALANCE SHEET — PROFITS 1 05 

ance the cost or credit side with the asset or debit side of the 
balance sheet. This rate would in most instances include a 
fraction or decimal, such as 4.27 per cent. The rate which 
thus balances cost and income is the rate of interest earned by 
the investment. And since money is never borrowed at odd 
rates, and the earning power of an investment does not deter- 
mine the rate of interest used in calculating its value (§62), 
these items of cost and value seldom balance exactly, but always 
show a profit or loss. 

Yet the fact that this rate exists indicates a second method 
of determining enterprisers' profits. The rate earned, expressed 
in terms of compound interest, eliminates the element of time 
as effectually as does discount, and enables the investor to com- 
pare the income rather than the expectation value of two in- 
vestments. The forest investment must earn p per cent before 
it becomes as desirable as the money it represents. If x per 
cent is earned, then when x per cent > p per cent the excess 
represents the ratio of profit or enterpriser's gain, per dollar 
of investment, in excess of the standard rate. If x per cent 
< p per cent, the rate x per cent still indicates net income, 
but compared with p per cent, there is a loss, or rather a failure 
to realize the amount desired. 

122. Profits in Destructive Lumbering. — It is assumed that 
owners who do not intend to continue in forest production will 
sell the land or devote it to some other purpose. Its sale or 
appraised value for this purpose is credited as income. 

Let P = profit. 

P = Y ■\-S,-{C + S,) i.op- - E (i.op- - i) 

= Y-\-S, + E-{C-\-S,-\-E) i.op\ (H) 

This formula is expanded, by the addition of other items of 
both cost and income, to the form, 

P = Y + Ss + E + Tp {i.op--^) -f T, (i.o^-') 
+ Tr (i.op--^) - (C + 5, + £) i.op- 
- Q (i.op'^-') - C, (i.o^"-«) - Q (i.op^-f). (Hi) 

This formula gives the profit on a single stand of timber, 
for the year of sale, assuming that both timber and land are 



Io6 FOREST VALUATION 

sold, or that the timber is immediately removed and the land 
sold or appraised. 

Actual profits on the investment in land and timber exclusive 
of lumbering, for a large operation, must be based on actual 
sale of land rather than appraisal at time of sale of timber, 
and if this sale is delayed, as it may be, for many years, the 
transaction is not closed. A new account may be opened for 
the denuded land, crediting it to the original account preferably 
at the cost, not the present sale value of land, and debiting 
the land account with this investment. If a "cost" account is 
kept as before, the land will be charged with interest until sold. 

123. Profits on a Stand of Timber. — Whether or not the 
owner intends his land for future crops of timber, the profit on 
the existing stand may be separately stated, by charging interest 
on the cost of land as an expense against the timber, and credit- 
ing the land at its original cost, when the timber is sold. 

P = F + 6", - (C + 5,) i.op^ - E {i.op- - i) 

= F + 5, + E - (C + 5, + £) i.op\ (K) 

This formula differs from H only by the introduction of Sc 
as an asset in place of S^, and may be expanded in the same 
manner as Hi. 

124. Anticipated Profits on Young Timber. — Assuming that 
Sc is credited at the time the timber is cut, the profits of that 
year may be anticipated for the year a in one of two ways. 
The net profit (K) may be discounted to the present (II), or 
the balance may be struck for the given year by direct compu- 
tation of value and cost for that year. In the latter case, 

Value = ^ + ^'^-^^ _ (5 + E). 

Cost = (C + 5, + £) i.op° - (5, + £). 

^ = ^^t-t^ - (C + 5, + £) ^.op\ (KO 

i.o/>" " 

This formula may be expanded by the addition of income 
and cost items, regardless of whether these costs occur after 
the year of valuation, or income occurs previous to this year. 



FOREST STATICS — BALANCE SHEET — PROFITS 107 

T 
The expression ^ gives the present equivalent of Tp in the 

year a whether a > p or the reverse. Therefore, 



,r— a 



I.O/?"~" I.O/?P~" I.O/?«~" I.O^'" 

- (C + 5, + £) I. or - C, (1.0^-'^) 
-C(i.o/^— ) -Q(i.o/^''-0. (K2) 

125. Profits from Continuous Forest Production. — If in- 
stead of abandoning the business, forest production is to be 
continued, the sale value S, credited for land does not express 
the true conditions. The value S^, representing the expectation 
value of the soil or the value of all future crops, must be sub- 
stituted for S,. 

Formula H then becomes 

P^Y + S, + E-{C-\-S, + E) i.op\ (L) 

The net profits from future crops, expressed as 
Y -C 



I. op" 



-iC + E), 



may be substituted for the expression 5„ in the formula, which 
does not alter the result. Both the net profit on the present 
crop, and on the future crops, S^, should include all items of 
cost and income which appear in Formula Hi, but the repetition 
of these terms in Formula L has been omitted. 

126. Anticipation of Continuous Profits. — To anticipate the 
total net profit, for the year a, including net income from all 
future crops, the value 5„, once determined, is substituted for 
Sc as an asset in Formula Ki which then reads 

^ = ^"^t-t^ - (C + 5. + £) i.op^. iU) 

i.o^" 

This formula is modified by the same additions for extra items 
of cost or income, as Formula K2. But Formula Ki gives the 
profit on the present stand of timber, exclusive of future crops 
or of profit on the sale of the land, while Li includes these 



Io8 ; FOREST VALUATION 

future profits. Should Formula Li be derived in the same way 
as Ki the result stands 

^ = ^tor-^ - (C + 5e + £) I .or - (5. - S.) , 

which indicates a means of separating the profits on the stand- 
ing timber from that on the future crops, or ''soil," parallel to 
the method employed for sale values in § 123. 

The true derivation of Formula Li is from value (§ 116, D2) 
and cost (§105, A2) of the entire property, timber and soil. 

Then 

P = ''¥,- "F,. (L2) 

127. Profits Expressed in Soil Values. — In the year in 
which the enterprise of planting or reproduction is undertaken, 
and previous to the actual planting, the net value of all future 
income is S„, or, expressing this value as discounted from future 
crops, it equals 

Y — C 

— — - (C + E). 

i.op" - I 

The cost includes merely the price paid for the soil Sc. Then, 

P = S,- 5e. (L3) 

Since this profit is shown for the year previous to undertaking 
forestry, it is taken as an indication of the advisability of such 
an enterprise. This relation shows clearly the nature of S^, 
which is merely a calculation of discounted net income. S„ 
does not indicate what a purchaser should pay for land. It 
indicates the highest price which he can afford to pay and still 
expect to earn the desired rate, p per cent, on his undertaking. If 
more than this is paid, a prospective loss is incurred, i.e. he 
cannot expect to earn as much as p per cent. If the land costs 
less than S^ he has good prospects of earning a profit at p 
per cent, or a rate of income, x, exceeding p per cent on his 
investment. If a purchaser is so foolish as to deliberately 
convert his expected profits {S„ — Sc) into costs, by making 
Sc = S^, he is merely handing over these profits to the one who 
sells him the property. 



FOREST STATICS — BALANCE SHEET — PROFITS 109 

5„ increases in value with every change in prospective in- 
come or expenses which alters the net value of this income, 
and is much larger for soils of good than poor quality. But 
there is evidently no profit in devoting to forestry lands which 
will sell for other purposes for a sum larger than 5„. 

In countries where forestry is extensively practiced on lands 
owned by states, or on private estates which have practically 
never changed hands, there is no way of determining the cost 
of land. The value of the soil, Sy, is calculated for the pur- 
poses of taxation and as a necessary step in valuing growing 
timber. This value may be recalculated at any time. It is 
evident that the soil value may always be placed at a figure 
which will permit the investment to earn exactly the rate of inter- 
est agreed upon as the standard for forest investments. And 
in practice, if during the crop period it becomes evident through 
price changes or other influences that the investment, with its 
former soil value, will earn more than p per cent, this value 
is promptly raised, and the rate of earnings is thus arbitrarily 
reduced to p per cent once more. The real status of the in- 
vestment is thus concealed in the capitalized value of the soil. 
Applied practically to a private operation, this process would 
consist of entering the land in the capital account as an asset 
having a value in excess of its cost. If this value were made 
great enough, the investment never could earn more than p per 
cent upon said value. But figured on the original cost, a much 
greater rate of profit may be shown. This practice of capital- 
izing income as soil value is universal in European forest finance, 
and the profits of forestry, standardized to p per cent, may be 
discovered only by comparing the values of land computed for 
different sites and species, and by a knowledge of past changes in 
these soil values. 

If S^ equals Sc, it may be substituted for Sc in Formulae A, 
Ai and A2. This is done under the conditions just discussed, 
where Sc is not determinable. The effect of this substitution 
is to make the computed cost of timber in any year of the rota- 
tion just equal to its expectation value in that year, and to 
reduce profit, outside of soil value, to zero. 



no FOREST VALUATION 

In the same way, it can be shown that for definite costs and 
income, the profit determined for any year may be converted 
into that for any other year by the use of Formulas I and II. 

Substituting 5„ for Sc in Formula Li, thus reducing profit 
to zero, this formula becomes 



I. op" 
Then 



-{C + E)= 5„. 



i.o/>" 
Resuming the value of Sc as cost of land, the profit is 

P = ^ + ^^ + ^ -{C + E)-Sc 
I. op" 

= 5„ — Sc. (See L3.) 

Since Formulae Li and L3 are thus derived from Formula L 
by discount (II), the reverse is true, and for any year a 

P = {S,-Sc)i.op\ (L4) 

128. Profits Expressed as a Ratio of Income to Capital. — 

The economic forecast shows profits as a net sum or balance 
between assets and cost, which sum cannot be realized in money 
without a sale of ownership. But the net future income which 
is accountable for this balance of profit shown may be also 
expressed in terms of interest earned on the cost instead of as 
capitalized value (§121). The rate or ratio of income to capital 
depends directly upon the period of time elapsing between ex- 
penditure and income (§ 23), a fact often lost sight of. In quick 
profits, earned largely by the sale of property at an advance in 
capitalized value rather than by awaiting the slow reahzation 
of income, the element of time is lost sight of; yet every profit 
should be standardized by reducing it to the rate of interest 
which it represents on the investment for the period of waiting. 
Should a property be sold at double its cost, the profit is 
100 per cent on cost. But with the element of time intro- 
duced, the rate earned would be as follows (Formula XIV) : 



FOREST STATICS — BALANCE SHEET — PROFITS 



III 



Sale at end of 


Rate earned, 
per cent. 


I year 

5 years 

lo years 

20 years 

50 years 

100 years 


100 

14.9 

7.2 

3-6 

1-4 

•7 



129. Earning Power of Capital Invested in Forest Produc- 
tion. — In no form of business does the per cent earned by the 
total amount of capital invested equal the per cent earned by 
the proprietor's investment unless he furnishes the entire capi- 
tal without borrowing (§32). 

In business receiving annual income, the capital needed to 
carry the current expenses is usually borrowed, and therefore 
does not share in the profits but receives p per cent only. 

These arguments are used as a justification for separating the 
capital invested in a forest crop into two portions, one of which 
shall be computed at p per cent, and not share in the profits, 
while the remainder is the basis upon which the rate of income 
is computed. By thus reducing the amount of profit-sharing 
capital, the rate of profit is increased or reduced on this capital 
as the earnings exceed or fall below p per cent on the total in- 
vestment. 

For instance, it may be arbitrarily assumed that the owner 
acquires the land, but borrows the funds needed for all expenses 
of crop production (Group A, § 104), as silvicultural expenses, 
and maintenance or annual charges. It has been shown that 
such a transaction would seldom occur. But if it does, these 
expenses must first be returned from income, with compound 
interest at p per cent. The remaining sum is net income 
earned by the owner's capital, Sc. 

Net earnings = Y + S, - IC (i.o/>") + E (i.o/>" - i)\ 
= Y + S,-\-E-{C + E)i.op\ 

The substitution of Sc or of S^ for S^ will adjust this formula 
to any desired condition (§§ 122, 123 and 125). 



112 FOREST VALUATION 

In this formula, E = , and as p is determined, this term 

o.op 

has a definite value (but see Formula N2). 

Capital invested by owner = Sc, 
Rate earned = x per cent, 

Period of time = n years. 

By use of Formula XIV (§ 89), 

5c (i.ox") = F + 5, + £ - (C + £) i.op'^, 

,.o^n ^ (F + 5.+£)-(C + £)i.or (N) 



or X = 100 



\ ;/ F + 5,+£-(C + £)i.or _ ^ ; 



This division of capital is purely arbitrary. An equally 
justifiable assumption is that the owner also invests the capital 
needed for silvicultural operations and all initial expenses (Group 
B,§ 104). In this case, the borrowed capital E is first repaid 
with p per cent interest from the gross income and x per cent 
determined for the remainder. 

Net earnings = Y -\- S^ - E (i.o/>" - i), 

Capital invested by owner = Sc + C. 

Then {Sc + C) 1.0:1;" = F + 5, +£-£ (i.op-), 

,,,„^ F+5.+E^-^E(r.or) ^ (NO 



;/ F+5, + £-£(i.or) , I 

or :r = 100 ) Y c _i_r V ■ 

Both of these solutions (N and Ni) give a value for a:, 
greater or less than that actually earned by the entire capital 
investment. The difference is greatest when only the investment 
in soil is used as a basis. Method Ni has been advocated for use 
in this country.* 

The true "economic" percent (§121) earned by an investment 
is the rate paid on all capital invested for periods of one year or 

* Forest Management of Loblolly Pine, Bulletin 11, U. S. Department of Agri- 
culture, W. D. Sterrett, Jan. 23, 1914, p. 21. 



FOREST STATICS — BALANCE SHEET — PROFITS 113 

over, regardless of ownership. This investment must include 
the annual expenses which are not cancelled by annual income. 
In this case, 

Net earnings = Y -\- S^, 

Capital invested by owner = Sc -\- C -\- n (e) (see § 105). 

Then net earnings = Y -\- S, - HSc + C -{- E) i.ox" - £|, 

„ Y + S, + E f^. 



. "/ F + ^, + £ ) 

But in this formula, E = , and as x appears on both sides 

o.ox 

of the equation, a solution is not reached. The value of x may 

be obtained by trial. A trial per cent x' is first substituted for 

X in the expression and the value E' determined. The 

o.ox 

solution then gives a value x" . This new value is then sub- 

stituted for x' and 77 gives E" . The second solution of the 

o.o:r 

equation will give a value for x usually within one-tenth of one 
per cent of true value. 

This result is satisfactory, for the rate, x, is a prediction or 
estimate in most instances; or where results are at hand, it is 
merely a calculation intended to gauge the relative merits of 
the investment compared with others. For such purposes, even 
^ per cent is sufi&ciently close. 

In the solution of the value of x, the use of logarithms is not 
usually necessary. The value may be found ui Table VI, op- 
posite n years, and interpolated to one-tenth of one per cent. 

This method of gauging the profits of forest production is far 
more suitable to new conditions characteristic of the industry 
in America than the method of capitalizing income in the form 
of soil value or computing the "forest per cent." In ahnost 
every instance, except for lands owned by the nation, the cost of 
acquiring the property is known, or is a determining factor to 
be decided previous to undertaking forestry. It is upon this 



114 FOREST VALUATION 

investment that profits must be computed whether or not the 
capital invested in future expenses is also entitled to share in the 
profit. The rate of interest earned offers an intelhgible standard 
of comparison with the common forms of business enterprise. 

The profit (§ 39) or enterpriser's gain is then found as a ratio 
instead of a lump sum, by subtracting p per cent from x per cent. 

European methods of computing the rate x earned by capital 
invested in forestry differ from those advocated above. The 
capital investment is regarded as the cost of the forest soil, 
in accord with Method N. But instead of computing the rate 
of compound interest which is earned on Sc, the first step is to 
calculate the annual "rent" earned on S„, which is equivalent 
to S^ X o.op. This, divided by Sc, gives o.orc, and x is termed 
the mean annual forest per cent. As expressed by Schlich, 

x = ^Xp. (N3) 

The per cent x in this formula is more sensitive than in 
Formula N. When x > /?, a higher rate is shown for x than that 
given by method N. This is due to the effect of using different 
rates of interest, x versus />, in discounting by the two methods. 

Formulae N to N3 express profits only for the beginning of 
the enterprise, as forecasts or as summaries. When the poten- 
tial annual or current rate of interest is desired, termed the cur- 
rent annual forest per cent, this may be found, after the timber 
becomes of merchantable value, by first determining the annual 
increase in this stumpage value (Chapter XII, § 182). 

Let F„ = stumpage value in year n. 

F„+i = stumpage value in year w + i. 

From the increase thus shown must be deducted the annual 
expenses e. The investment consists of the cost of the forest 
for the year w, consisting of soil and timber, and represented 
(Formula A.) by "Fc. 

The formula for current forest per cent is 

'^-:/""> °° (NO 



FOREST STATICS — BALANCE SHEET — PROFITS I15 

for which may be substituted 

^ = i ^^-r^:r' \ 100. (N.) 



5o + F„ 

For a normal forest (§ 109) the forest per cent is obtained by 
methods identical with those appHed in Formulae N3 and N4. The 
value of such a forest (F2) divided by its cost, which is either 
the cost of purchase or of production (§ 109), gives the basis for 
the following formula 

x = ^Xp. (Ne) 

130. The Relative Importance of Profits in Private versus 
Public Forestry. — In Chapter III it was emphasized that for 
very long periods the operation of the laws of compound in- 
terest requires the lowering of the rate of interest, "/> per cent," 
used to gauge the relative value of investments. It is easily 
shown that enterprises running for periods of over 50 years 
cannot earn to exceed 4 per cent except under the most favor- 
able circumstances, although the specific net profits above 
cash outlay may exceed this outlay by several hundred per 
cent (§§53 and 128). 

Private industry cannot be expected to undertake the business 
of forest production on a scale commensurate with our future 
needs, for the following reasons: 

1. A higher rate of interest is required on private than on 
public undertakings. 

2. The average business life of an individual is shorter than 
the period required to produce a forest crop. 

3. The private enterprise depends for its existence solely on 
profits, while the public undertaking includes the benefit to the 
community as the principal item of income, and may therefore 
be conducted at an actual money loss and still be justified. 

4. In many instances, lands are already the property of the 
state or nation, and no cost or interest on land need be charged. 
The sole cost of public forestry in such instances is the sum of 
actual outlays for protection and silvicultural measures. 

5. PubHc forestry can and should be conducted on a very 



Il6 FOREST VALUATION 

large scale as it is on the national forests, with resulting economy 
in all measures of protection, technical administration and 
improved efficiency which will increase future revenue. 

6. Private ventures are based on the assurance of an enter- 
priser's gain or net profit above p per cent, which is a matter 
of indifference in public enterprises. The necessary lowering 
of the interest rate on long investments, the postponement of 
results and the increasing importance of the governing rate of 
interest as affecting the size of the indicated profits lessen the 
individual's interest in forest production as a business venture, 
and strengthen the reasons for state or national enterprise. 

After the forest capital has been destroyed, its restoration by 
planting or seeding can be of interest to private owners only 
for species, regions and sites which promise reasonably quick 
returns and high values, such as are shown for white pine in New 
England or Loblolly pine in Maryland. But before destructive 
lumbering has made such restoration necessary, especially for 
forest§ which show a succession of age classes, such as spruce in 
the northeast, the private owner may often continue to operate 
indefinitely, with profit, by removing only the more mature 
timber. This difference is due to the fact that such a forest 
produces income annually with which to cancel expenses. Under 
such circumstances the specific balance sheet shows an annual 
profit; there is no accumulation of unpaid interest, and by fore- 
going the "profits" he might obtain at any time by withdrawing 
the entire capital, the owner substitutes a permanent annual 
income. 

In considering questions of public policy, no sound conclusions 
can be reached if the financial questions involved are neglected. 
The difficulties of inducing private owners to voluntarily enter 
forest production as a definite business are evident. If this 
course is made mandatory by legislation, as is seriously contem- 
plated in some states, it must first be shown that the expenses 
thus required are in reasonable relation to the income that can 
be expected from forestry. Otherwise it would appear that the 
state is attempting to shift onto private shoulders a responsibility 
which it should pubhcly assume. 



FOREST STATICS — BALANCE SHEET — PROFITS 117 

This public sentiment for regulation is the expression of an 
instinctive protest against destructive lumbering as a policy, 
for it is far more expensive and wasteful to tear down a busi- 
ness and then rebuild it than to continue it as a going concern. 
Whether or not forest owners can afford any other policy than 
destructive lumbering, they should in any case use every effort 
to do as httle harm as possible to reproduction, protect cut-over 
lands from fire, and induce the formation of a new crop of natural 
seedlings on absolute forest soils. In proportion to the effective- 
ness of such measures for perpetuating the productiveness of 
forest lands in private hands, the desire on the part of the public 
for drastic interference with private rights will lose its force. 

131. Forms for Specific Accounts in Forestry. — The accounts 
kept by the proprietors of a large business, involving the owner- 
ship and management of many separate parcels of forest land, and 
a more or less continuous annual income and outlay, must show 
specifically the cash transactions and actual cost of the property. 

The capital accounts should record cost of permanent assets. 
But to this cost may be added the annual excess of actual cash 
expenses over annual income, incurred for the care and mainte- 
nance of the property (§57). The only alternative is to exhibit 
a corresponding deficit in the balance sheet. The choice between 
these methods will be based on the character of the assets. 
For property increasing in value by natural growth of timber 
there can be no serious objection to the process of adding actual 
costs to the capital account. 

A depreciation fund is seldom required for such an enterprise. 
The equipment subject to depreciation is of such small total 
value that it will usually appear as expense. 



BALANCE SHEET 



Assets 
Capital assets: 
Land. 
Timber. 
Other property 
less depreciation. 
Current assets: 
Cash. 
Accounts receivable. 



Liabilities and Proprietorship 
Capital paid in. 
Surplus. 

Loans (liabilities). 

Current liabilities: 
Accounts payable. 



ii8 



FOREST VALUATION 



TRADING, AND PROFIT AND LOSS ACCOUNT 
A. — Land 



DeUt 

Cost, to date of sale. 
Balance, gross profit, to general outlay 
and income account. 



Crtiit 

Sales. 

Balance, loss, to general outlay and in- 
come accoimt. 



Debit 

Cost, to date of sale. 
Balance, gross profit, to general outlay 
and income account. 



B. — Stumpage 

Credit 

Sales. 

Balance, loss, to general outlay and in- 
come account. 



C. — General Outlay 

Debit 
Silvicultural operations. 
Protection. 
Maintenance. 
Administration. 
Taxes. 

Loss, from lands. 
Loss, from timber stimipage. 
Balance (profit). 



AND Income Account 
Credit 
Leases. 
Grazing. 

Secondary forest products. 
Thinnings. 
Profit, from lands. 
Profit, from timber stumpage. 
Balance (loss). 



Balance (loss). 

Interest on loans. 

Depreciation. 

Surplus (profit for period). 



Balance (profit). 



Deficit (loss for period). 



CAPITAL ACCOUNTS 
D. — Land. 

Debit 
Cost, by parcels. 

Additions to cost by reason of annual 
cash expenses. 



Credit 
By cost to date of sale. 
Balance. 



Debit 

Cost, by parcels. 
Additions to cost by reason of annual 
cash expenses. 



E. — Stumpage. 

Credit 
By cost to date of sale. 



Balance. 



p — Distribution of Annual Loss, from Profit and Loss Account 



Debit 



Deficit. 



Credit 
By increase of capital assets. 



FOREST STATICS — BALANCE SHEET — PROFITS 
G. — Distribution of Surplus 



119 



Debit 



To dividends. 



Credit 
Surplus, profit and loss account. 



H. — Changes in Value of Capital Assets 



Debit 
Appreciation or marking up of value of: 
Stumpage. 
Land. 



Credit 
To appreciation of assets. 



Depreciation of assets. 



To losses of timber by reason of fire, 
etc., not insured. 



132. Forms of Economic Accounts in Forestry. — During 
the formative or constructive period of a forest investment, 
previous to the receipt of the principal income, the economic 
status of the entire investment may be shown by a cost account, 
in which accrued interest is charged against all outstanding 
capital investments. 



Debit 
Outlay for all sources. 
Accrued interest on outlay. 



Outlay and Income Account 

Credit 
Income from all sources. 
Accrued interest on income. 
Balance, representing net investment 
or cost. 



Since such an account is intended merely for the owners' in- 
formation, the "interest" cost is a legitimate one. In the same 
way the "economic" balance sheet (§ 73) can be made up by 
discounting the value of future income and entering the assets 
on the basis of their capital or expectation value. 



"Economic' 



Debit 



Balance Sheet 

Credit 
Total net cost of land and timber from 

outlay and income account. 
Net cost of improvements (original 
cost, less sums returned for de- 
preciation). 
Potential surplus. 

It is this balance which is the object of nearly all the calcu- 
lations discussed under forest finance. 



Expectation value of land and young 

timber. 
Value of improvements. 
Potential deficit. 



CHAPTER IX 
THE APPRAISAL OF DAMAGES 

133. Principles Underlying Appraisal of Damages. — In ap- 
praisals to determine damages, the principles underlying the 
valuation of forest property reach their fullest development 
and receive their most complete application. When the eco- 
nomic basis of forest valuation is understood (Chapter IV) it 
will be seen that the guiding principles of legal practice indicate 
a consistent effort to apply this basis in determining compen- 
sation for damages. 

The uncertainty and difficulty of authoritative determination 
of future values is here, as elsewhere, the most serious drawback 
to the unqualified adoption of expectation values as the basis 
for measuring losses or damages. Whatever substitute methods 
are adopted, as, for instance, the determination of cost, are dic- 
tated by the greater relative certainty of the figures thus ob- 
tained, which consideration may outweigh in importance the 
fact that these figures do not accurately represent actual value 
or loss. 

These legal principles may be summarized as follows: 

a. Damages are payable in money. Compensation, not 
physical restoration, is required. 

h. The difference in value of the property before and after 
the damage is the measure of damages. The value of the por- 
tion destroyed is not in itself the measure of damages, but is 
a means of ascertaining this difference in total value. Soil and 
timber are real estate. The value of this real estate as a whole, 
before and after the injury, is the measure of damages. 

c. Damages must be appraised on the basis of the most prof- 
itable use to which a property is adapted, as indicated by the 
use of similar contiguous property. Sale value may or may not 
be a correct index of real value. 



THE APPRAISAL OF DAMAGES 121 

d. Values must ordinarily have a commercial or utilitarian 
basis, but aesthetic values, or the value of "legitimate gratifi- 
cation" (§ 4), must be recognized whenever based on elements 
generally accepted by the pubHc at large. Sentimental value 
peculiar to the owner cannot be admitted. 

e. Loss of income may be made the basis of damages; but 
this loss should be discounted to the present, and will then equal 
the loss in capital value. 

/. Cost of restoration, while frequently ruled out, is admitted 
when shown to be less than value, or when value is difficult to 
determine. 

g. Ordinary "profits" or income is the basis of damages. 
Excessive profits, which do not allow for normal losses, and 
speculative or contingent profits, which depend upon uncertain 
future factors, such as increased prices, are not admitted. The 
element of time, intervening between the damage and the real- 
ization of profit, does not bar the consideration of these profits 
provided they are reasonably certain to occur and are properly 
discounted. 

h. Damages must be actual, present, imminent or reasonably 
certain to occur. The damage itself may be indirect, but it 
must be proximate, or traceable directly to the offending cause, 
as, for instance, the destruction of crops, due to cattle, through 
leaving a gate open. The physical destruction of property by 
fire is an actual present damage. The cause may be a spark 
from a defective locomotive igniting the debris upon an improp- 
erly cleared right of way, several miles from the property 
destroyed. The determination of the money value of the dam- 
age is the only element of uncertainty in the process.* 

* The entire subject of damages is the source of wide differences of legal opinion 
and practice in different states. Precedents and rules adopted in one state are 
frequently at variance with the decisions in other states. The measurement of 
damages is largely a determination of facts rather than of legal principles; the 
ascertaining of the amount and character of the injury done to the property and 
consequent income of the plaintiff. The above rules appear to agree with the 
principles laid down in Sedgwick on Damages, gth Ed., Vol. 3, §§ 931 to 933. 
The contention of foresters that expectation value, where it can be determined, is 
the basis of damages, finds its clearest legal expression in rule b above, in which 
form it is receiving increasing recognition in state courts. See reference above for 
citations of cases. 



122 FOREST VALUATION 

134. Elements of Damage to Forest Property. — Damage 
may occur to forest property through injury or destruction of 
timber, soil or permanent and temporary improvements. For 
permanent improvements, the cost of replacement or repair is a 
fair basis of valuation. For temporary improvements, the present 
value would be found by subtracting depreciation from cost, or 
estimating the future usefulness of the improvements destroyed. 
The problems discussed in this chapter are those which deal 
with damage to timber crops and forest soil. 

The separate elements which may constitute damages are 
itemized as follows: 

Mature timber. 

Young or immature timber. 

Forest soil. 

Watershed protection. 

Reduction in total value of property not otherwise damaged. 

Ji!sthetic values. 

135. Physical Separation of Timber from Soil. — Damage 
to forest property may take many forms, but only those sources 
of injury traceable to human agencies financially capable of mak- 
ing good the loss, are of interest in appraisal of damages. All 
losses involving actual destruction of property are irreparable 
in the sense that the entire value destroyed is lost to some 
person. Losses from insects, wind or disease must be appraised 
for the information of the owner. But when the loss is to be 
shifted to another, and collected by legal processes, its appraisal 
must rest upon facts that can be accepted by a jury. 

Timber trespass takes the form of removing forest products 
from the soil without the consent of the owner and, incidentally, 
of injury thereby caused to unmerchantable trees. The main 
element of damage is the value of the timber destroyed or taken. 

Damage by fire results in the destruction, or partial destruc- 
tion, of the tree growth, or merely in injury and retardation of 
growth. Except in the most unusual conflagrations, the timber 
even if completely killed is not consumed or removed in the sense 
that it is in lumbering. Much of this fire-killed timber, if large 



THE APPRAISAL OF DAMAGES 1 23 

enough to be merchantable, can be salvaged. After the great 
fires of 19 10 in the Pacific northwest about 90 per cent of fire- 
killed timber owned by private parties was marketed. If not 
merchantable, the inflammable dead material, rotting and fall- 
ing, greatly increases the fire hazard (§ 200). In practically no 
case does fire bring about a complete separation of the timber 
from the soil. 

136. Separation of Value of Timber from Value of Soil. — 
As a step in the appraisal of damages it may be necessary to 
determine separately the value of timber and of soil. 

By Formula G the separate value of timber is 

Y + S^-hE 



I.C/)""" 



-(S,-\-E), 



which gives the value in the year a for the timber by sub- 
tracting the value S^ from the total value of the property. 
The residual value, land, then equals S^, and if the damage just 
equals the value of the timber, it may be appraised by this 
means. But this assumes that the physical separation actually 
takes place, and that the soil or property 5„ is left, as a result, 
in the same condition which it would be in after lumbering and 
brush disposal. This premise becomes evident by analysis of 
the above formula which equals 



= ( 



i.op"-^" \ i.o/?"~"/ V I -Op" 

Y + S^-^E 



i.op" 



-E -S„ 



In this form the separate values of land and timber are clearly 

shown. But the expression S^ ^^ is equivalent to the 

difference in value of Sy if freed for use now, and its present 
value if freed for use only after the lapse of n — a years. 
This difference is equal to the present, discounted or capital 
value of the interest on 5„ for n — a years, or 

5, (i.o/^-'-" - i) 



124 FOREST VALUATION 

It is important to understand the significance of this treat- 
ment of soil value in valuing timber. One way of describing 
this "expense" is that the owner of the timber is charged with 
the interest on the soil value, or "soil rent," as a cost of bringing 
the timber crop to maturity, dating from the present year. 
This is the assumption made by Schlich.* This would class 
soil rent as an actual future cash expense similar to taxes. But 
soil rent cannot be an actual future cost or outlay, unless a differ- 
ent person owns the soil and rents it to the one who grows the 
trees. The capital value of the property, timber and soil, takes 

no account of this cost (Formula Do) for ^^ is the dis- 

i.op" " 

counted net income, which constitutes soil value. 

A separation of the present net value of the standing timber 

from the value of subsequent crops (soil S^) gives 

F + £ 



i.op"' 



— E = value of timber, 

S 
^^ = present value of soil if released in n — a years. 



I. op 
Comparing this with 

F + 5, + £ 



— (Sy -\- E) = value of timber, 



i.o/>"~' 

S^ = value of soil, 

the sum of values for soil and timber, or the value of the property, 

is identical, but the proportion of this total value assigned to 

the timber is greater by the first method than by the second, 

by just the amount of the discounted interest on 5„. 

In the second method, instead of assuming that the timber 

owner is charged with interest on 5„, a much clearer conception 

is that the land owner, who in fact is the same person, benefits 

by the release of his land value from its necessary use for w — a 

years to produce the revenue F. He therefore cannot de- 

Y 4- E 

mand the full value — — E for the crop, but accepts a 

i.o/>" " 

value smaller by the exact amount of the excess in value of 

* Schlich's " Manual of Forestry," 4th Ed., Vol. Ill, Part II, Chapter III, p. 133. 



THE APPRAISAL OF DAMAGES 1 25 

S^ over ^^- The trespasser, in settling the damages, thus 

" purchases " the timber separately and is given the benefit of 
subtracting the discounted future expense of "soil rent" in re- 
duced damages. It is now possible for the owner to obtain 
this soil rent on another crop of timber that can be planted 
immediately. He is not justified in collecting it in the form of 
increased net damages. 

The subtraction of soil rent from present value of standing 
timber in appraisal of damages is therefore a mere matter of 
book-keeping between the owner and the trespasser, by which 
the owner is the loser in damages, but is compensated by the 
release of the land. 

It is evident that unless these conditions are actually secured, 
and the land not only released from the crop but left in the con- 
dition which would normally result from logging, such an as- 
sumption absolutely fails to appraise the true damages, which 
are in excess of the amount indicated. 

In European practice, the expectation value for the soil S^ 
is first computed. This value is then introduced not only in 
determining expectation value of standing timber, but is also 
substituted for the cost of the soil. 

The effect of using Sy as the so-called "cost" of the soil is to 
eliminate "profit" or enterpriser's gain, and to balance costs and 
income at p per cent (§127). Not only will the costs balance 
the income at the final year, but, by formula Ki, substituting 
5„ for Sc, 

^ i"l^l-t ^ - (Sv -hE) = (C-\-S^-\-E)i .op^ - (5„ + E) , 

which indicates that this so-called "cost" is exactly equal to 
expectation value of timber for any year during the growth of 
the crop. This means that if actual cost of soil is not known, 
or does not enter into the problem, as in the case of govern- 
ment lands, and the returns from forestry are computed on the 
basis of a fixed rate of interest, p per cent, throwing all "profit" 
into terms of soil value (§ 127), standing timber of a given age 



126 FOREST VALUATION 

will have the same value whether computed as a cost or as a 
capital value. To compute this value under actual conditions 
in this country, either the standard rate of interest for many 
sections must be very low or a negative soil value may have 
to be used, which is perfectly practical. The method is so 
foreign to our ideas of finance that it should be discarded in 
favor of the more intelligible plans of utiUzing actual costs and 
sale value, or of discarding altogether the subtraction of inter- 
est on soil as a deduction from damages. 

137. A Basis of Damages : Cost of Replacement. — The 
objections to the use of cost of replacement as a measure of 
damages are that it does not represent the true value of the 
property nor measure the loss (§§i33&, 68). Its merits lie in the 
certainty of the figures, derived as they are from past experience. 

Very young timber or reproduction may be completely de- 
stroyed by fire. It has no sale value, except, rarely, for Christ- 
mas trees. The expectation value of such young stands is 
difficult to compute. But the cost of planting and the annual 
charge for protection and administration can be easily deter- 
mined. 

Assuming that the trees have been completely killed and that 
no further expense is needed to prepare the ground for a new 
crop, the cost, including interest on soil, the use of which is 
lost, will be, for a years, 

(C + Sr + E) I .op" - {S. + E) . (A) 

By substituting the capital value of soil for 5,-, this cost be- 
comes equal to the expectation value of the young timber 
(§ 127). But this value 5„ is even more unreliable than the ex- 
pectation value of the young stand (§116). If Sc is charged 
as a cost, it will be determined by the price paid for the soil, 
or the sale value of similar bare land in the vicinity. 

Where, as in government forests in the west, land has no 
purchase price, the practice is to omit this item from cost. The 
cost of the crop then becomes 



THE APPRAISAL OF DAMAGES 1 27 

The effect of this omission is to decrease the damages demanded. 
The cost C is included except when natural reproduction is 
sure to occur. In this case, C may be omitted, and the damages 
would then amount merely to the annual expenses 

Eii.op" - i). 

In ordinary cases, the entire annual charges, including admin- 
istration, taxes and upkeep, would constitute the cost. But in 
national forests, administration expenses are frequently offset 
by revenues from grazing, while taxes are not paid. The item 
e may then include only the cost of fire protection. The rate 
of interest adopted in government forestry is seldom over 3 
per cent. For these reasons, damages based on cost for private 
forests usually exceed those claimed for government timber of 
the same quality. 

Excessive costs of replacement are sometimes demanded on 
the basis that the trees burned should be physically replaced 
with others of like size. An owner who has a young grove 
destroyed feels that the small value represented by the cost of 
growing the trees does not compensate him for the loss of the 
grove. His trees are gone and he will have to wait an equal 
period for a new plantation to attain like size. If repeatedly 
burned, he would never secure his grove. The excess value 
indicated in such a case actually exists, both as sentiment on 
the part of the owner and as an addition to the value of the 
entire property (§ 133^). Neither of these elements are best 
valued by attempting to estimate the cost of immediate physical 
restoration of the property, but are discussed under other head- 
ings (§§ 138 and 147). 

With increasing age of the timber, the relative merits of cost 
as a basis, compared with value, become less and less. Wherever 
there is a marked divergence in the two, whether cost exceeds 
or is less than value, the collection of damages based on cost 
cannot be justified by any principle of law. Its use is clearly 
a make-shift and will be confined to young timber whose age 
does not exceed one-half the period required to bring the trees 
to maturity. 



128 FOREST VALUATION 

138. A Basis of Damages : Sale Value. — Sale value is a far 
more reliable indication of damage than cost. In forest property, 
it is always a question as to whether the timber destroyed or 
removed can be valued separately, and by this means the loss 
in value to the property as a whole be determined. 

The ultimate sale value of the timber is a reliable basis for 
damages, as it is the basis of capital value not only for the tim- 
ber but for the soil as well (Chapter VII). Whenever timber 
is destroyed which has a present sale value, this value must be 
ascertained, and will be accepted as the measure of damages 
for the timber destroyed, unless it can be proved that other 
damage has been suffered. If the timber is young and growing 
rapidly, or if it is at present inaccessible but certain to be de- 
veloped in the near future, its present stumpage value or sale 
value may not represent its true value to the owner, who intends 
to hold it. By proving with reasonable certainty the existence 
of this higher value, sale value even for merchantable timber 
can be set aside. But the burden of proof is on the owner, and 
courts will accept sale value for timber unless a strong case for 
higher values can be shown. 

The loss in sale value of the entire property is not so easily 
gauged. It is a great advantage to be able to value the income, 
in the form of timber, rather than to judge of the effect of this 
loss of timber upon the selling value of the property. In theory, 
the latter loss more accurately gauges the damage (§ 1336). 
There are cases when the value of the materials destroyed is 
wholly inadequate as a measure of the loss resulting to the 
owner. 

The most direct case is where a portion of a large stand is 
destroyed, appreciably reducing the total amount that may be 
logged. This raises the cost per thousand feet, or unit, for 
logging the remainder (§§ 98 and 174). The increased cost is 
subtracted from stumpage value of the remaining timber. The 
total loss is equal to the sale value of the timber burned plus 
the loss in sale value for the entire remaining body of timber. 

A woodlot frequently adds materially to the sale value of a 
farm. Its destruction would represent a loss many times greater 



THE APPRAISAL OF DAMAGES 129 

than the value of the wood, and, under definition b, this difference 
in value for the entire property must be the basis of damage. 

For such losses, affecting the value of the entire property, 
the appraised loss in sale value is the safest guide, as it eliminates 
sentiment or personal considerations (§ 12,3d). 

Were the general public fully alive to prospective values of 
young timber and of forest lands, and agreed upon the rate of 
interest which should apply to forest investments, and if a suffi- 
cient movement in forest real estate existed so that these opinions 
could be crystallized by sales, there is no doubt that sale value 
for immature timber would approximate its real value so closely 
that it might be accepted as a basis for damages as readily as 
the sale value of mature or saleable trees. This would be an 
immense advantage, as there is never any objection to accept- 
ing sale values whenever they are evidently just to the owner. 
But with the growing of trees as a business still in its infancy, 
or perhaps not practiced at all, the sale value of such young 
timber is likely to be far below its capital or expectation value. 
Under principle c (§133) a great injustice would be done the 
owner by accepting such a basis of settlement. 

In regions where immature timber is commonly regarded as 
having little if any value, the claimant must prove the injus- 
tice of such valuation by demonstrating his intention and ability 
to bring the young trees to maturity and to realize the ultimate 
revenue. It would be difficult for a lumberman who customarily 
abandons his lands to fire, to do this. But the United States 
Forest Service has no trouble in proving the value which it 
places upon such young growth. In regions where forestry is 
extensively practiced, and upon lands which the owner has had 
under management, such as plantations, not only will sale value 
more nearly approximate real value, but it will be easier to secure 
the true expectation value independent of the standard set by 
sales. 

139. A Basis of Damages : Expectation or Capital Value. — 
Not only does sale value fail to establish the value of property 
to the owner for his own use, when this value is unfamiliar to the 
public at large, but it frequently happens that there are no sales 



130 FOREST VALUATION 

of similar property on which to base such values. There is a 
further difficulty in judging of the loss in sale value resulting 
from the damage. For these reasons, and in order to base the 
damage fairly upon loss in income or use, the capital value or 
expectation value of the property, as well as of the portion de- 
stroyed or income lost, must be calculated, in spite of its uncer- 
tainties. These uncertainties (§ 67) He in the determination of: 

Future yield of merchantable material. 

Date of maturity or final cutting. 

Future price of products. 

Rate of interest adopted. 

Authoritative studies of the yields per acre for important 
commercial species are becoming available which indicate not 
only the amount of merchantable material to be expected, 
but the proper age at which to cut the stand. In the absence 
of such data, experience of farmers and woodlot owners in re- 
gions of second growth can be cited. 

It might seem that the certainty of the upward tendency of 
prices for wood products would justify the adoption of higher 
stumpage values as a basis of damages for destruction of young 
timber (Chapter XII). This argument is ingeniously used by 
the Forest Service to justify valuation of very young timber on 
the basis of cost and thus secure higher values than would be 
shown by capitalizing income on the basis of present stumpage 
prices. It is probably true that owners forced to accept settle- 
ment on terms of expectation value based on present prices, 
for timber which will not mature for several decades, are losing 
a profit which in all reason they may expect. But the deter- 
mination of the amount of this increase introduces a speculative 
element into a calculation already sufficiently complicated, and 
runs directly counter to principle g (§ 133). Damages are in- 
tended to fully compensate the owner for reasonable profits, 
and no objection can be raised to admitting the effects of the 
growth of the timber or its increase in quality, but the fluctua- 
tion of stumpage prices will not ordinarily be admitted by a court 
and it is the part of wisdom to base the evidence upon prevailing 
prices. In such calculations as an owner may make for his own 



THE APPRAISAL OF DAMAGES 131 

information, he is at liberty to speculate on the increase in 
prices as he sees fit. 

The rate of interest will remain a matter of dispute until 
forest production takes its place as a recognized business. The 
higher the rate used, the smaller and more conservative will be 
the value placed upon the damage. This is directly opposite to 
the effect of a high rate used in calculating cost of replacement. 
In such a case, the higher the interest rate, the greater will be 
the cost, and the smaller the value of the crop (§ 121). 

140. Damages to Merchantable Timber. — Timber killed by 
fire is saleable if accessibly located and a market exists capa- 
ble of absorbing it before it deteriorates from rot and insects. 
If sales can be made, the damage is the difference in value of 
the timber before and after the fire. To this loss must be added 
the loss in stumpage value of timber not burned but whose 
logging costs are increased as a result of the diminished quan- 
tity of stumpage (§ 138). 

Let y = value of damaged timber, 

L = total damage. 

The loss is expressed as 

L = Y -Y\ (0) 

Timber cut illegally may be settled for with or without suit, 
on the basis of the stumpage value.* But it is poor satisfaction 
to an owner to collect merely the present value for small timber 
which he desired to preserve. Additional damages can be ob- 
tained by the owner, if he can prove: 

a. That the expectation value of the timber is greater than 
its present stumpage value. Unless increase in prices is per- 
mitted, this is not always easy to show. 

b. That the sale value of the entire property has been in- 
jured by the cutting. 

* An important principle of damages widely recognized is that in case of 
wilful trespass, the value of the products wherever found, is the measure of the 
damages. In such cases the value of the timber after felhng, transportation, or 
manufacture may be the basis of damages. Sedgwick on Damages, 9th Ed., 
Vol. Ill, §934. 



132 FOREST VALUATION 

c. That its value for other uses, as park purposes, has been 
injured. 

He may also instigate a criminal action against the perpetrator 
provided the trespass is wilful. In case of a logging contract 
under which the contractor is required to leave trees of certain 
sizes, constant inspection by the owner, cancellation of the 
contract, or perhaps a clause requiring payment of double 
value for forbidden timber is more effectual than damage 
suits. 

Merchantable timber injured by fire but not killed must be 
appraised on the basis of its present saleability, and the extent 
and character of the damage to its sale value. If it can be sold 
at once, the loss will be measured by deterioration in grade 
and quantity due to the fire. If it must remain for some years, 
a further deterioration may be expected as the result of fungi 
and insects. If this can be measured, it should be allowed. 
Timber whose sale is necessarily postponed, even if of mer- 
chantable size, should be valued by the same method as young 
or immature timber. Its expectation value, as reduced by rot 
and insects, and not its present sale value, should be the basis 
of damage. 

141. Damage to Immature Timber: Partial Loss. — For 
reasons given in § 138, sale value for immature timber de- 
stroyed does not compensate the owner, and it rarely happens 
that the sale value of the property, either before the damage 
or after it occurs, is a safe index of the damage. Cost of 
replacement may be used, as suggested in § 137. But for 
timber more than half grown or approaching maturity, capital 
or expectation value must be the means of approximating the 
loss in value to the property, and this method should always 
be used as a check on cost, even for very young stands. 

Where a stand is injured but not killed, the trees will continue 
to occupy the soil until they reach merchantable size and are 
cut. The damage to the crop is measured by the loss in value 
of the timber when cut, traceable to the fire. 

Y = original expected value of timber when cut, 
F' = expected value as reduced by fire damage. 



THE APPRAISAL OF DAMAGES 133 

The future net value of each of these crops in the year n is, 
respectively, when 5 represents either Sc, S^ or Sg, 
Y - (5 + E)(i.or-«- i), 
r -(5 + E)(i.or-"-i), 

as the expenses continue undiminished. The difference in net 
value, representing damages, is F — Y' . Discounting this loss 

Y - Y' 

to the present year a gives — • (Oi) 

Under normal conditions, the expected value of the crop cannot 
exceed 

Y - (5 + £)(i.o/'"-»- i). 

But if F'< (5 + E) (i.o/?"-« - i), 

then Y -Y'>Y -{S + E) (i.o/)"-« - i), 

and damages will exceed the expectation value of the timber. 
That this result coincides with actual conditions can be easily 
shown. A damaged crop of timber which will just pay expenses 
can be left till mature. But what is to be done with a stand 
damaged so severely that it will not meet these future expenses? 
Its presence prevents the use of the land for a new crop, yet the 
cost of removing it is a net loss. Assuming that the timber 

Y - Y' 

will be left standmg, should be used whenever Y' can 

be determined. The total loss to the value of the property 
rather than to the timber is thus measured (§ 1336). 

142. Damage to Immature Timber: Total Loss. — When 
immature timber is totally destroyed or so badly injured that it 
must be removed if any further profitable use is to be made of 
the soil, two factors influence the method of appraisal. The 
soil is released by this removal, and its value advanced from 

S 

^ to 5„ (§ 136). But the value S^ is materially altered 

i.op^ ° 

to the injury of the owner. As S„ is merely the value of the 

discounted net income, all future expenses directly diminish 

this value, as is seen in the formula for S^ or 

V — C 

I. op"— I 



134 FOREST VALUATION 

The initial expense C includes brush disposal, soil prepara- 
tion, and the cost of securing reproduction. The removal of 
burned and worthless timber increases C abnormally. The 

c 

expense E representing includes fire protection. A fire 

o.op 

trap, caused by debris, must either be removed as an initial 
cost or an additional annual expense e' be incurred, propor- 
tionally increasing E to E' for at least a few years. 
If the value of the burned timber is appraised as 

Y + S^-^E _^s^^E), 



i.o/>"~" 

the owner must be left in possession of a value for land, S^, un- 
diminished by such expenses (§ 136). The expense of restoring 
this value is (C -f E') - {C -\- E), in which (C -|- E') repre- 
sent the costs of securing and protecting the new crop after the 
fire.* For instance, should natural reproduction, by sprouts or 
seed, be the normal method, but as a result of the fire, planting 
becomes necessary, the cost of planting constitutes a damage. 
If the owner would have had to plant anyway, the damage in- 
cludes only the cost of removing the debris or protecting the 
plantation from extra fire hazard. 

The damage where young timber is totally destroyed may be 
summarized as: 

Timber destroyed = "-z {S^ + E), 

Further damage to property = 5, — S'^, 

Total damage = ^ + -^"_+-^ _ (5; + £) . 

I. op" " 

In other words, the value of the soil resulting from the fire can 
be substituted for its value previous to the fire, thus covering 
the total loss in value of the entire property. But as (C'-f- E') — 

* This formula is technically incorrect, since the additional expense e' — e 
endures probably for but a limited period b. Hence the increased cost of this 
item is (£' — E) {i.op'' — i) instead of (£' — E). This alteration may be made 
in formula O2. 



THE APPRAISAL OF DAMAGES 135 

(C + E) as an expense is the equivalent of S„ — S'^ in future 
value, the practical application of this problem consists in es- 
timating the costs of restoring the soil to its original condition, 
5„, and adding these future costs to the value of the timber 
destroyed. It must be emphasized that this is not an awarding 
of double damages but that the two items are absolutely distinct 
and their sum represents the loss in value of the property. The 
formula should, therefore, be expressed, 

L = ^ + ^^ + ^ + c' + £' - (C + E). (Oo) 

i.o/?" " 

The cost of removing dead timber and debris and any extra- 
ordinary cost of securing reproduction is thus seen to be a legiti- 
mate damage wholly apart from and in addition to the value of 
the timber destroyed. 

143. Damage to Forest Soil. — Damage to the soil results 
frequently from fire, and sometimes this is so serious that the 
soil is entirely destroyed. This damage takes two forms, 
actual physical injury by destruction of litter, humus and 
beneficial bacteria with resulting impoverishment of the soil, 
and loss of profits or net income from either present or future 
crops of timber, without necessarily injuring the soil itself. Both 
results usually occur and there is no accurate way of measuring 
the injury to the soil, in terms of money, except through loss in 
probable income from timber crops. 

Damage to soil resulting in destruction of litter and humus, 
but which does not kill the standing or growing trees, results 
in retarding their growth. This decreases the volume and value 
of the crop. The damage is measured by the reduced value of 
the standing timber (§ 141, Oi). 

Damage to soil accompanied by complete destruction of 
timber can be measured only by the probable effect of this 
injury on the value of a new crop of trees. When the soil is 
largely vegetable, as in swamps or on high mountain slopes, its 
destruction, especially on slopes, may prevent all further tree 
growth. The damage then equals 5„ in addition to the value 
of the timber burned. When the soil is partially destroyed, 



136 FOREST VALUATION 

it will be difficult to estimate accurately the probable loss on a 
new crop, unless the effect of similar burns can be cited. 

The cost of restoring soil value by removal of debris (§ 142, O2) 
is wholly apart from the appraisal of physical damage to the 
soil itself. Except in unusual cases, this physical damage is 
exceedingly difficult to measure in terms of value, and, where 
timber is destroyed, destruction of soil represents but a small 
proportion of the total loss. This item of damage is, therefore, 
neglected in most instances. 

144. Damage to Single Trees. — When the expectation 
value of young timber is made the basis of damages, and the 
present value of future crops is calculated, the future expenses 
deducted from value are based on the acreage protected and 
utilized by the crop. The yield of the timber is also computed 
on the basis of area, and in this way the normal loss in numbers 
which occurs in all stands with increasing age is allowed for. 

In scattered stands of timber, the individual tree becomes 
more important, and this importance increases in stands com- 
posed of trees of many ages. Damage or loss in such forests 
cannot as easily be appraised as for crops of even-aged trees. 
The mature timber can be estimated according to its merchant- 
able contents. If these trees are still small, though merchant- 
able, it may be possible to show that their future increase in 
volume and quality, with consequent increase in value, is such 
that this discounted value exceeds the present value of the 
trees. 

If it be assumed that all trees now merchantable will remain 
standing, and future expenses are neglected, the expectation 
value so obtained will be too high. Such figures must be reduced : 

By allowing for loss of numbers; 

By pro-rating the crop expenses among the reduced stand, per 
tree, according to present volume. 

The immature portion of such stands cannot, with any degree 
of accuracy, be valued on the basis of individual trees. The loss 
in numbers previous to maturity increases with decreasing age, 
and the proportional expense to be charged to each tree becomes 
wholly problematical. 



THE APPRAISAL OF DAMAGES 



137 



145. Damage to Many-aged Stands. — The value of damage 
to a many-aged stand is determined by the character and value 
of the stand. Should the timber be entirely destroyed, its value 
corresponds to that given in §117 or §118, according to the 
age classes represented. The keynote in valuing damage to 
stands containing both immature and mature trees of different 
ages on the same area is to attempt to separate the stand into 
its age classes according to the area which each really occupies. 
This permits of the distribution of future costs and avoids 
double valuation. 

For instance, suppressed and stunted reproduction growing 
under old timber may be considered as occupying little if any 
area. But if this reproduction would have been the means 
of forming a second crop after logging, it must be valued. Its 
age should be taken not as the actual age resulting from sup- 
pression, but as the age of trees of similar size grown in open 
land. Means of determining accurately the proportional areas 
occupied by age classes in such forests are not yet perfected. 
But an approximation of the area and average "economic" 
age of the crop, or age of an even-aged stand of equal volume 
and sizes, is the only satisfactory basis for arriving at damages. 

The first step is to decide upon the area which should be 
assigned to immature timber as a whole. The remaining area 
is that occupied by mature trees. The appraiser then decides 
whether to divide this immature timber into several age classes, 
or to assume an average age for the entire crop and treat it as 
an even-aged stand of that age. If more than one age class is 
required, the area and average age for each is determined. In 
this manner the even-aged stand and area become the basis of 
appraisal of damages for many-aged forests (§140 to 142). 

146. Damage to Watersheds. — The protective value of 
forest cover affects, first, the soil itself and its ability to produce 
timber crops, and second, the property and interests affected 
by stream flow. 

Soils subject to erosion may be completely ruined, even for 
tree growth, by the effect of removing the timber cover through 
fire or logging. This loss would be measured as in § 143. 



138 FOREST VALUATION 

But the damage inflicted on other property caused by the in- 
creasing irregularity of stream flow, floods followed by almost 
complete cessation of flow, the silting up of streams and reser- 
voirs, and the consequent damage to navigation, waterpowers, 
irrigation and agriculture are additional to the loss of the timber 
and soil on the property itself. DeHberate ruin or removal of 
necessary timber cover, and destruction of grass and brush by 
over-grazing, probably renders the owner of such lands liable for 
the resulting damages to others. But the connection between 
cause and effect, while proved beyond a doubt, is very difficult 
to express in money value. Large areas of watershed contribute 
to the result, and the damage extends over many years and 
varies according to rainfall and other circumstances. To deter- 
mine the proportion of this ultimate probable damage for which 
the denudation of one acre is responsible, is a mere guess. Such 
protective areas should be acquired by national or State govern- 
ments and the damage prevented, rather than to attempt to force 
private owners to preserve the forest for the benefit of others, 
or endeavor to collect damages from such owners for the in- 
juries caused by their abuse of the forest cover. 

In the absence of commercial value, as where forests are in- 
accessible and cannot be cut, the cost of re-establishing the 
protective cover, either by natural or artificial means, and of 
protecting this area from fire until it reaches the same state of 
effectiveness as that which was removed, can properly be con- 
sidered as a measure of damages. It is also possible in the case. 
of forest users, such as lumbermen, to set an arbitrary value per 
acre for the protective influences of the cover, and bind the user 
by private contract to pay this sum in case of fire occurring 
through the carelessness of his employees. 

As knowledge of the effect of forests on flow of streams is ob- 
tained, it will become possible to arrive at a value per acre of 
the protective influence of the forest cover on different water- 
sheds. This value may then be used in damage suits. 

147. iEsthetic Values. — The fundamental character of the 
value represented by an appeal to the aesthetic sense must be 
recognized in appraising damages (§ 4). The gratifications for 



THE APPRAISAL OF DAMAGES 139 

which mankind will pay money are by no means confined to the 
material demands of the body. Simply because it is difficult 
to place a money value upon such gratification is no reason 
for denying its existence. Scenery and beauty are capitalized 
by those who provide hotels and camps for visitors, and the 
common rights in scenery, especially in the enjoyment of woods 
and forests, clash repeatedly with the private property rights 
of those who own and may wish to cut the timber, usually to 
the loss of the public, without recourse to damage suits. Such 
rights, just as in the case of watersheds, are best protected by 
public ownership of lands and forests which have peculiar or 
exceptional value. 

But the private owner who has acquired property of scenic 
and aesthetic value is not obliged to accept merely the commer- 
cial value of the income from wood products as full settlement 
for damages caused by fire or theft. The additional value is 
as real to him as similar values are to the public at large. It is 
just this common or universal acceptance of this form of value 
which permits of its appraisal as an element of damages. Pur- 
chasers can usually be found for estates possessing such advan- 
tages, and at prices which would probably compensate the owner 
for any reasonable cost he has incurred to secure the results. 
For this reason, the aesthetic values destroyed may frequently 
be gauged roughly by the loss in sale value of the entire prop- 
erty. Where landscape features are affected the damage can 
best be appraised by experts familiar with landscape gardening 
rather than forestry. 

148. Punitive Damages. — Damages in excess of loss in 
value are sometimes provided for by law in case of destruction 
of property belonging to the state. This is not justified by 
any principle applicable to private owners, but is rather an at- 
tempt to enforce punitive measures as a matter of public edu- 
cation. It lies halfway between civil judgments and criminal 
penalties, in which the offender is punished as a public example. 
The state of New York has such a law, providing a penalty of 
$10.00 per tree destroyed on the Forest Preserve. The advantage 
of combining punitive measures with civil suits for damages is 



-I40 FOREST VALUATION 

extremely doubtful, and in suits instituted by New York, this 
provision, while held as a club over the heads of the offending 
parties, has not been used as the basis of determining the dam- 
ages. Even in private contracts it has been found advisable 
to secure compliance with contract terms by other means than 
the enforcement of punitive damages for unauthorized acts. 



CHAPTER X 
FOREST TAXATION 

149. Sources of Revenue from which to pay Taxes. — Taxes 
are levied to raise funds with which to meet the expenses of gov- 
ernment. They therefore constitute an annual charge against 
the wealth of the community. In both theory and practice 
taxes are levied against persons instead of property, and are 
gauged according to ability to pay, and not on the basis of 
benefits received. But the effect of taxation upon the value 
of productive property may best be studied by regarding the 
enterprise as the source of the revenue required to pay the 
taxes. The expense of taxes must be met eventually from 
income, as are all other annual expenses. Taxes must be paid 
whether or not this income from the taxed property is forth- 
coming, and in the absence of such revenue, or previous to its 
receipt, must be met by the investment of additional capital 

(§ 131)- 

Such investments of capital add nothing to the value of the 
property, and must eventually be recovered from income. 
Should the taxes reach a proportion where the entire net income 
is absorbed, the property becomes worthless to the owner (§ 61) 
and will be abandoned, as was the case with much cut-over 
timberland in the Lake States in the early '90's when owners 
could see no prospect of income sufficient to pay the annual 
taxes. 

150, Tax on Income. — A tax on income is the most logical 
method of preventing excessive taxation. The relation between 
the income and the tax is definite and the collection of the tax 
follows the receipt of income, thus relieving the owner of the 
necessity of borrowing or making additional unprofitable invest- 
ment of capital. The determination of net income raises the 
question as to the character of expenses to be permitted as deduc- 

141 



142 FOREST VALUATION 

tions from gross income. A tax levied on gross income must of 
necessity be at a lower rate than one levied on net income, and 
is more easily computed. But net income is a more scientific 
basis of taxation since the net, after subtracting expenses inci- 
dental to securing it, is the only portion of gross income which 
becomes the property of the owner available to meet taxes. 

151. Tax on Value of Property. — Value of property is de- 
rived from net income (§ 64) and may therefore be taxed directly, 
without injustice, provided the assessed value of the property 
does not exceed its expectation or capital value, and the rate 
of taxation on this capital value bears the proper ratio to the 
legitimate tax on income. 

This ratio is dependent on the rate of interest used as the 
standard for determining the capital value {p per cent). The 
annual equivalent of intermittent income may always be found 
(XIII). The relation between this annual income and value is 

_^ , Income 

Value = 

.op 

= Income X ^• 

P 

The expression is the ratio between a tax on income and on 

capital value. It follows that a tax equal to a per cent of value 

must take X a per cent of income. A tax rate of 10 mills, or 

P 
I per cent, when the rate of interest is 5 per cent, will require 

X I per cent, or 20 per cent of the income, while a 20-mill tax 

5 
absorbs 40 per cent of income. With a rate of interest of 10 

per cent the proportion of taxes to income would in this case be 
respectively 10 per cent and 20 per cent. 

The amount of the annual tax is the product of the assessed 
value and the tax rate. The annual tax, rather than either the 
rate or the assessed value alone, determines the relative per cent 
of income demanded. A low valuation permits a proportion- 
ally higher tax rate, while high tax rates may be lowered with 



FOREST TAXATION 1 43 

no corresponding reduction of taxes by increasing the assessed 
valuation. 

In practice, sale value is made the basis of valuations for 
assessment purposes, and since sale value may not coincide with 
expectation value (§§ 17, 59, 69), this may cause both assessed 
value and taxes to depart widely from the desired ratio. 

A tax on sale value secures the desired ratio of net income 
most accurately when property is producing this income annu- 
ally. When the income is intermittent and deferred, great dis- 
crepancies and inequalities are almost certain to exist in the 
ratio between taxes and final income. 

152. Taxable Value of Property. — The taxable value of 
property is the value determined from future net income, or its 
capital value (§ 62) calculated by disregarding the future expenses 
represented by the proposed taxes, but deducting the discounted 
value of all other future expenses. The net income which rep- 
resents this net value is then divided between the owner and 
the taxing power, and the owner's final net income is what is 
left after paying his taxes. 

153. Effect of Taxes on Property Values. — This net taxable 
value is merely the sum of values belonging jointly to the owner 
and the taxing power or public. Nominally the complete 
ownership is vested in the proprietor. Practically the power 
to take income carries with it and is a manifestation of the sov- 
ereign right of ownership, and on failure of the owner to pay 
taxes this right is exercised by confiscating the property. But 
the payment of the tax results no less in an actual transfer of 
value from owner to public. The residual value after sub- 
tracting the taxes from net income is the real value of the prop- 
erty to the owner, who is justified in considering it as worthless 
when the total net income is absorbed by taxation. 

It might be assumed that in absence of taxation, property 
would be worth the additional value represented by the capi- 
talized taxes. This is Hterally true when property is exempted 
from taxation and at the same time receives all the benefits of 
governmental activities. Just as business expenses are expected 
to result in income greater than the expense, so the benefits of 



144 FOREST VALUATION 

a government conducted by and for the people, and respect- 
ing the rights of property, should, on the whole, give a full 
equivalent in service for the taxes collected. Whatever the 
effect may be upon the individual property owner, the entire 
level of values is raised and the pubhc or common share in this 
increase should absorb less than the total gain. 

Perfect equality of taxation on all forms of income and capital 
value would have no visible effect upon relative values of dif- 
ferent forms of property. But if the burden of taxes is un- 
equally distributed, either by deHberate intent as is proposed by 
the advocates of single tax on land, or by exemptions of certain 
forms of private property from taxation, or merely by reason 
of the imperfect working of the machinery for assessment and 
collection of taxes, this balance is disturbed. The value of 
property over-burdened with taxation is then confiscated in 
actual reality and to just the extent of the excess of taxes above 
the average level. This serves to depress the sale value of the 
property and lower its apparent taxable value, resulting either 
in diminished taxes or an increased tax rate which still further 
depresses values. The end of the vicious process is physical 
confiscation of the property, destruction of the private enterprise 
dependent on it, and the cessation of public revenue from taxes 
formerly received. Meanwhile, property bearing less than its 
share of taxes is automatically increased in value and made 
prosperous at the expense of the over-burdened forms of enter- 
prise, but only to a certain extent, for the effect of the destruction 
of any form of industry is a general lowering of the value of 
all forms of property or of the total wealth of the community. 
Universal equality in taxation on the basis of ability to pay 
(§ 149) is, therefore, the goal of all genuine efforts at tax reform. 

154. The General Property Tax. — The general property 
tax is a direct tax levied on the assessed value of all forms of 
tangible and intangible property on the theory that equality 
in taxation is thereby secured. In an agricultural age and 
region results were fairly equitable. With increasing complica- 
tion of modern industrial development, the method has become 
less and less effectual, since it fails to secure equal proportions 



FOREST TAXATION 145 

of net income from different forms of property and industry. 
As a means of taxing standing timber, it is a conspicuous failure 
in this respect, as the tax rates and the total taxes paid on 
timber bear no fixed relation whatever to the ultimate value of 
the income. 

155. The Problem of Taxation for Timberlands. — The 
failure of the general property tax when applied to timberlands 
is due to several causes. Imperfect and unequal valuations 
are more prevalent with this class of property than with other 
forms, owing to the inherent difficulty of estimating and apprais- 
ing standing timber and the unfamiliarity of tax assessors with 
this work. This is not a defect of the system, but merely in 
its application. 

There are three fundamental difficulties in securing equitable 
taxation of timber under this system, namely: 

The difficulty of distinguishing capital from income for pur- 
poses of taxation. 

The practice of collecting taxes in advance of the receipt of 
income. 

The element of time and the resulting problem of interest in 
its effect on the relation between taxes, income and taxable 
value. 

156. Distinction Between Capital and Income in Timber 
Property. — Regarded as a crop, artificially produced, the en- 
tire value of timber represents the income earned by the capital 
invested in the soil. In the form of an even-aged stand, the 
increasing value of the crop is merely the accumulating income 
which, when finally cut, exposes the soil capital once more 
(§116). In determining the value of this soil capital, all future 
expenses are deducted at compound interest. The annual in- 
come equivalent to this final income (Formula XIII) is termed 
soil rent, and the point of view which regards soil alone as capi- 
tal, timber as income, and requires all values to be based on 
compound interest, is termed the theory of soil rent. 

In contrast to this conception, land and timber together may 
be regarded as capital. A forest which has been brought to a 
condition of complete normaUty (§ 109) capable of yielding a 



146 FOREST VALUATION 

continuous annual income without diminishing the value of the 
capital, has an actual capital or property value which includes 
the entire value of all stanchng timber. The annual net cash 
income from this forest represents interest on this entire forest 
value, and is termed forest rent. As this income cancels annual 
expenses, compound interest on the forest as a whole has no 
chance to accumulate. The point of view which regards the 
forest, including timber, as capital, and does not deduct com- 
pound interest on costs but treats the entire forest as a business 
capable of producing annual net returns, is termed the theory of 
forest rent. 

The latter conception more nearly approximates the attitude 
of investors in American forest property. Yet both the con- 
ditions and the thoughts of investors occupy a position midway 
between the extremes of soil rent and forest rent. Timber is 
almost universally acquired in the form of native or virgin 
stands, already grown, and is purchased as capital. The entire 
business, rather than the stand, or parcel, is the basis of annual 
income, if such income is secured. The source of this income 
is largely the increase in value of the timber, rather by price 
increment than through growth, and in the realization of this 
income the capital itself is liquidated (§132). The operation 
thus resembles a speculation similar to the holding of unim- 
proved real estate, rather than a productive business as contem- 
plated by the idea of forest rent. Under such conditions, the 
distinction between capital and income cannot be co-ordinated 
with the physical distinction between wood and soil, or between 
wood capital and wood increment. It is a mere matter of book- 
keeping based on cash investments and cash returns. 

157. The Problem of Interest in Forest Taxation. — But the 
problem of interest appears in such investments in the form 
presented by the distinction between the theories of soil rent 
and forest rent (§35). When the investment as a whole pro- 
duces no annual income for a period of years, unearned interest 
on the annual expenses accumulates and this time element affects 
both final "cost" and capital value of the property. 

The capital value of a forest which will produce a sustained 



FOREST TAXATION 147 

income which is realized at intervals greater than one year, may 
be less or greater than that of a forest producing income of the 
same total value, but in annual installments. The difference 
in value is due to the same factors which cause the difference 
between soil value and forest value, i.e., the income is discounted 
by compound interest, and the discounted total of future or 
intervening annual expenses is deducted from value. 

As touching taxation the question assumes this form: Shall 
taxes be levied on actual present value of property, or shall 
deductions from this value be permitted, including interest on 
past costs, in arriving at the net taxable value? And shall 
taxes paid in advance of income be computed as if drawing 
compound interest in calculating the per cent of final income 
which such advance payments of taxes absorb? 

158. Effect of Present Condition of Forest upon Choice of 
Methods of Taxation. — These problems are best presented by 
a concrete example in which the effects of the two opposing 
theories are illustrated. 

A stand of Loblolly Pine in Maryland * yields products 
worth on the stump: 

At 20 years of age $17.81 per acre. 

At 30 years of age 61.14 per acre. 

At 40 years of age 108.91 per acre. 

At 50 years of age 168.49 P^^* acre. 

Land costs $5.00 per acre. Annual expenses, exclusive of taxes, 
are 3 cents per acre. The cost of securing reproduction is placed 
at $5.00 per acre. 

An interest rate of 5 per cent will be assumed for the problem. 

A tax rate of 20 mills on full value will be assumed. This 
is nearly twice as heavy as the average rate, yet it is exceeded 
in many forest regions, especially in new and poorly developed 
localities. 

The area of the forest will be taken as 50 acres, and the total 
yield in 50 years will be 50 X I168.49 or $8424.50. Three 
cases are assumed. Case A is for an even-aged stand cover- 

* Bulletin 11, U. S. Dept. of Agriculture, Jan. 23, 1914, Table 15, page 19. 



148 



FOREST VALUATION 



ing the entire area, and cut at the end of 50 years, thus giving 
the conditions described under soil rent. Case C is for a stand 
of all ages. There are here 50 age classes, each occupying one 
acre. The yield on one acre is cut each year perpetually. 
This crop may either occupy a separate area as an even-aged 
stand of one acre, or be scattered as single trees throughout the 
forest. The results will be identical. Case B is for a forest 
giving an intermittent yield every 10 years, thus presenting 
five age classes of 10 acres each. 

Except for this difference in the arrangement and present 
condition of the age classes of timber, the financial results for 
these forests are assumed to be identical. The capital value 
(expectation value) of each forest can be computed as a basis 
for taxation. 

Table II presents the relation between a tax of 2 per cent on 
capital value and an equivalent tax on income from sale of timber 
in each case. 

TABLE II 

Comparison of Results from Taxation of Capital Value of Forest Soil 
AND of Soil and Timber on a Forest of 50 Acres 





Basis of taxation. 


Character of 
forest. 


Cutting 
area. 


Period be- 
tween 
cuts. 


Value of yield 
for period. 


Cash expenses 
for period. 




Total 

for 
period. 


Per 

acre. 


Total. 


Per 

acre.* 


A 

B 

C 


Forest soiL 
Soil and timber. 
Soil and timber. 


Even-aged. 
5 age classes. 
All-aged. 


Acres. 
50 
10 

I 


Years. 

50 

10 

I 


$8424.50 
1684.90 
168.49 


$168.49 
168.49 
168.49 


$325.00 

65.00 

6.50 


$6.50 
6.50 
6.50 







* The cash expenses, $5.00 per acre for planting, and $1.50 per year, or $.03 X SO for protection 
of the entire tract, are charged against the area cut over within the period. 





Receipts less 
expenses. 


Cash expenses 

compounded to 

year of cutting 

at 5 per cent. 


Net value of 
stumpage. 


Capital value 

of property 

after removal 

of yield. 


Annual taxes 

at 20 mills 

on capital 

value. 




Total. 


Per 

acre. 


Total. 


Per 
acre. 


Total. 


Per 

acre. 


Total- 


Per 

acre. 


Total. 


Per 

acre. 


A 


$8099.50 
1619.90 
161.99 


S161.99 
161 99 
161.99 


$3180.87 

100.31 

6.50 


$63.61 
10.03 
6.50 


$5243.63 

1584.59 

161.99 


$104.86 
158.46 
161.99 


$ 500.95 
2519.62 
3239-80 


$10.02 
50-39 
64.79 


$10.02 
50.39 
64.79 


$ .20 


B 


1. 00 


C. 


1.29 





FOREST TAXATION 



149 



TABLE n. — (Continued) 





Total cash taxes 
for so years. 


Taxes compounded 

to year of cutting 

at 5 percent. 


Compound interest 
on taxes. 


Difference in taxes 

and interest paid 

on forests A and B, 

compared with C* 




On total 
area. 


Per acre. 


Total. 


Per acre. 


Total. 


Per acre. 


Total. 


Per acre. 


A 


$ 500.95 
2519.62 
3239.80 
2178.50 


$10.02 
50.39 
64 79 

43-57 


$2097 . 46 
3169. CO 
3239.80 
4326.50 


$41.95 
63.38 
64.79 
86.53 


$1596.51 
649.38 

2148.00 


$31.93 
12.99 

'■42:96' 


$1142.34 
70.50 


$22.84 


B. 


1. 41 


C 




A' 





(A'. Taxes levied on sale value, revalued at 20 years and every 10 years thereafter.) 
* This saving is largely due to the fact that the capital values of forests A and B are com- 
j?uted for the year in which these values are lowest, and remain at this valuation for fifty years. 
See §161. 

Per Cent of Values Taken by Taxation, Computing Taxes with Compound 
Interest to Year of Final Yield 





Full stumpage 
value. 


Net cash profit 
on stumpage. 


Net value of 
stumpage. 


A. . 


Per cent 

24-5 
37.6 
38.4 
SI. 3 


Per cent 

25.9 
39 
40.0 
53-4 


Per cent 

40 
40 
40 
82.5 


B 


C 


A' 





In the problem discussed, the tax rate of 2 per cent on full 
value is nearly twice the average rate of taxation on present 
values of forest property. But the crop of timber chosen as 
the basis of the problem is more profitable than that produced 
by most species and locaHties. The coincidence between total 
cash taxes for 50 years at 2 per cent and capital value would 
hold good only for the same period and rate, since 2 per cent X 
50 = 100 per cent of value. 

159. Scientific Taxation : Forest Property Tax. — The value 
given for the forest in case C is found by deducting the annual 
cash expenses, $5.0x3 for planting and 3 cents X 50 acres or 
$1.50 for protection. This gives $161.99 as the "net" value 
of the annual crop, which, capitalized at 5 per cent, equals 
$3239.50. (Formula XII.) 

The tax, 2 per cent, yields $64.79 annually. This is just 
40 per cent of "net" stumpage value and a slightly smaller 
per cent of sale value. The annual profit or net income of 



I50 FOREST VALUATION 

the forest coincides with net value of the yield, and the tax, there- 
fore, takes 40 per cent of this profit. 

Since no one would dispute the desirability of subtracting these 
current cash expenses previous to taxing stumpage value, it is 
evident that for forests producing an annual income, the tax on 
forest capital and on forest products are equal in value and inter- 
changeable. 

160. Scientific Taxation: Forest Land Tax. — The value 
given for forest soil in case A is found by discounting the value 
of the final crop for 50 years, treating it as a recurring income, 
and subtracting the discounted cost of planting and annual 
expenses in the same manner (§ 116). This gives $500.95 as the 
capital value of the soil just after removal of the crop. 

The tax of 2 per cent on this value for 50 years amounts, 
in cash, to but $10.02 per acre, as against a cash total of 
$64.79 P^-id by forest C. A study of the table explains this 
discrepancy. The sum of $31.93 represents compound interest 
on these taxes during the 50-year period. The further sum of 
$22.84 represents a saving due to the fact that the capital value 
adopted as a permanent basis for taxation is determined just 
subsequent to the removal of the periodic cut of timber. This 
requires that the future costs for planting and protection, amount- 
ing with interest to $63.61, be deducted from stumpage value 
previous to discounting (§ 105) to obtain capital value. 

As a result of this latter deduction or allowance, the total 
taxes with interest, paid on forest A, amount to but 25.9 per 
cent of the stumpage value minus cash expenses, or 24.5 per cent 
of sale value. The ratio of 40 per cent applies only to the 
reduced value or net profit on the investment in land. 

Forest B presents conditions midway between these two 
extremes. The capital value is found by discounting the de- 
cennial yield and deducting the discounted lo-year accumulation 
of expenses, giving a value of $2519.62 (§ 117, Fi). Upon this 
value a 2 per cent tax gives a total cash payment of $50.39 
per acre during the 50-year period, which is increased by com- 
pound interest to $63.38, leaving a small margin of $1.41 as a 
saving due to the factors explained for forest A. 



FOREST TAXATION 151 

In computing the comparative per cents of stumpage value 
taken by a 2 per cent tax on capital value, compound interest 
has in each case been added to the taxes, although this item does 
not constitute a cash outlay. It represents, rather, the equiva- 
lent to the community of receiving taxes in advance of income, 
or may be considered as the discounted value of a 40 per cent 
income tax paid in annual installments throughout the growth 
of the crop instead of at the close of the period. 

161. Comparison of Taxes on Forest Rent versus Soil Rent. — 
The point at issue between these two systems, both based on 
the taxation of capital value, is evidently the double deduction 
from income, first, of the future costs of production with in- 
terest, exclusive of soil, and second, of the interest on taxes 
paid previous to receipt of income. A forest created by plant- 
ing or human effort passes through stage A before it can be 
brought to condition C. Shall it, at the latter date, be taxed 
as for C or continue to pay the reduced taxes computed for A? 

This problem depends for its answer upon whether future 
conditions, or past conditions, are permitted to determine the 
burden of taxation. Both cases, A and C, as well as case B, 
represent actual present value, based on future conditions. 
When forest A is brought into condition C, its present value 
is no longer A but C and, based on value, it would pay the 
taxes demanded of C. 

Taxes are based upon value and not upon cost. Future 
costs diminish value (§ 64) but past costs are disregarded in com- 
puting value and do not directly affect it (§ 68). By this reason- 
ing, the increasing tax which would accompany increased capital 
value is apparently justified (§ 165). But just as property may 
have a definite value and still represent a net loss to the owner 
(§ 68), it may be shown that an owner of timberland cannot afford 
to pay taxes continuously for 50 years and then have these 
back taxes completely ignored and be taxed on the full value 
of his crop. The pubhc, basing the tax on present value, may 
ignore past taxes, but the owner, looking ahead, is not so apt to 
overlook this future possibility. This situation can only be 
met by a contract or tax agreement by which the public consents 



152 FOREST VALUATION 

to forego taxing the full final value C and confines its tax to 
present value A, in return for which concession the owner 
agreed to undertake the growing of the crop. Past errors in 
taxation will ordinarily have to stand. 

162. Scientific Taxation : Income or Products Tax. — The tax 
on income, correctly applied, is the mathematical equivalent 
of the tax on capital, provided the controlling rate of interest 
can be agreed upon. But the same difficulty is encountered 
in computing this tax as was detected in comparing taxes on 
forests A and C. Table II shows income taxes purporting to 
represent the equivalent of 2 per cent on capital value, yet vary- 
ing from 24.5 per cent to 38.4 per cent of the gross income. 

Net cash income from either form of forest. A, B or C, is the 
same, provided interest on expenses is neglected, and totals 
$161.99 per acre. The "net" income corresponding to the capi- 
tal value is diminished in cases A and B by deductions for 
interest, which accounts for these discrepancies. The question 
is, will such deductions be permitted in levying an income tax 
on present incomes? 

This question is open to the same solution as that proposed 
for the taxation of capital values. If the income tax is to be 
substituted for an annual capital tax on standing timber, the 
full rate can be levied without injustice. But if the income is 
not available until a distant future period on crops still immature, 
the lesser rate should be promised and contracted for as a future 
system of taxation binding on both parties. Future expenses 
must be considered in a scheme of taxation. Past accumula- 
tions of interest "cost" may be successfully ignored. 

This view is confirmed by the attitude of the U. S. Collector 
of Internal Revenue in interpreting the income tax on corpo- 
rations dealing in timberlands.* The ruling reads: "In cases 
where lands are purchased for cash, the cost being the proceeds 
of the sale of the capital stock of the company, the earning 
value of the money invested, that is, the interest which might 
have been received on this money had it been otherwise employed, 
cannot be added to the initial cost of the land to represent its 
* Letter, Jan. 6, 1914, to P. S. Ridsdale, Sec. American Forestry Association. 



FOREST TAXATION 1 53 

aggregate cost at time of sale. The compensation for such 
investment is the anticipated dividends which will be paid to 
the stockholders out of the profits when the lands are sold. The 
addition of the earning power of the money invested to the orig- 
inal cost of the lands would operate as a deduction of the divi- 
dend from gross income. Dividends are not deductible, either 
directly or indirectly. Interest purported to accrue on invest- 
ments of this character, made by stockholders, cannot be added 
to the initial cost of the assets for the purpose of fixing a cost 
price as the basis for determining the profits accruing to the 
corporation when such assets are sold." 

Since these regulations state previously that "the cost of 
assets (land and timber) for the purpose of determining the 
amount of income resulting from a sale is held to mean the pur- 
chase price of the lands plus the taxes and other carrying charges 
paid thereon prior to the sale," it is clearly the position of the 
government that interest on such carrying charges will not be 
permitted as a deduction from income. The national income tax 
on timberlands would, therefore, be based upon the theory of 
forest rent, ignoring interest, in spite of the fact that this income 
is deferred until some future year as in case A , and not earned 
annually as in case C. 

The tax would thus take the same per cent of income, whether 
this income were received in six months or sixty years. For a 
speculative business, where profits are not dependent on a definite 
period of time, this method of taxing income may not act as a 
deterrent. But with the production of forest crops, the announce- 
ment in advance that "no deductions from the income tax will 
be permitted for interest on future costs incurred in advance 
of income," would have a direct influence on future profits and 
act to prevent the undertaking. 

The controversy as to whether interest is a cost or an income 
as affecting taxation either of income or capital values cannot 
be settled, but may be dismissed, with this summary; past 
interest accrued on the capital invested by the proprietor or 
owner is not an actual cost, but merely a method of gauging 
profits and will usually be neglected in taxation. But future 



154 FOREST VALUATION 

interest, in the form of discount, cannot be neglected for it 
vitally affects present values, which are the basis of present 
taxation. Whether or not an income tax to be collected at a 
future period shall be reduced on account of deductions from 
income of interest on costs, depends upon the desirability of 
encouraging industry by granting this absolutely just conces- 
sion in advance. 

163. Scientific Taxation: Combined Capital Tax and Income 
Tax. — The two systems of taxation, capital tax and income 
tax, are thus seen to be interchangeable for property producing 
annual income (C), but to give widely divergent results for 
property whose income is intermittent {A). In the latter 
case, either system is open to grave objections. The capital 
tax can properly be computed only for the year following the 
yield, when it is most difficult to determine it exactly (§ ii6). 
The income tax wholly fails to satisfy the need for current 
revenue for which taxes are levied. The third difficulty is that 
during the growth of the timber and in absence of definite pro- 
vision to the contrary, the constant tendency will be to levy 
the capital tax upon the existing value of capital including the 
timber as if this temporary capital value were permanent and 
capable of producing permanent annual income (§ 156). 

In order to secure regular annual revenue from taxation 
in the absence of regular income from lumbering or cutting, 
and at the same time convince the public that owners of timber 
property are paying their full share of taxes, it is theoretically 
possible to assess the capital value of the property at a portion 
of its value and postpone the collection of the remainder as an 
income tax. 

In case A, the soil has a capital value of $10.02, but can be 
purchased at $5.00 per acre.* A tax on $5.00 at 2 per cent 
will amount in 50 years to $20.93, leaving $21.04 available as a 
tax on stumpage at time of cutting. This amounts in each case 
to 12.5 per cent of the ''gross" value, or 20 per cent of the 
"net" value of the yield. 

* This discrepancy in values is possible in regions where the value of land for 
forest production is not fully appreciated. 



FOREST TAXATION 1 55 

The true equivalents between capital tax and income tax, 
and the ratio of division between them, depend first upon the 
proportion of capital value which is taxed, second, upon the 
rate of taxation applied to it, and third, upon whether the com- 
munity is willing in the future to abide by its agreement and 
permit the owner to continue to pay taxes on the basis of 
capital values which no longer represent the present value of 
the property. If the rate is full, the only margin left for an 
income tax is due to a low valuation of the land. If the land is 
valued at its full capital value, only a reduced rate will leave 
a margin for income tax on stumpage. And in case the full 
rate is collected for the full period on its original capital value, 
the public is entitled to an additional income tax only by re- 
pudiating the owner's claim to deduction of interest on costs 
from gross stumpage value. In practice, capital values of land 
tend to advance and the stumpage tax might well be levied on 
the increased value of timber which is the cause of this advance 
in land value. 

In European systems of taxation both capital tax and income 
tax are usually levied, but the scientific relation between them 
is not determined. Each tax is assessed independently, but 
the combined taxes are sufficiently low so that the property is 
not over-taxed. 

164. Taxes under the General Property Tax. — Under the 
general property tax, the principle of taxing capital value, theo- 
retically the basis of the tax, is actually entirely superseded 
by the plan of taxing sale value regardless of income. While 
standing timber may be legitimately taxed as capital when, 
as in case C, only the annual growth is removed, the effect of 
annually taxing the sale value of even-aged crops is entirely 
different. The distinction between capital and income cannot 
be drawn with any accuracy. Case A presupposes that the 
entire timber value represents income only and not capi- 
tal. 

The injustice in the system consists in taxing annually, on 
its full capital value, a property which is not producing annual 
income, and which is being held and increased in value by a 



156 



FOREST VALUATION 



process similar to that of savings.* It is as if the owner of 
property capable of yielding a definite annual income of $168.49 
(Table II) allows this income to accumulate, although by so 
doing the earning power of the property is not increased. The 
tax assessor promptly adds this increment to the assessed value 
of the property, whereupon the owner, if he can, as promptly 
withdraws the surplus to escape this excessive tax. By inspec- 
tion of Table II it will be noted that the value of the yield just 
previous to cutting, for an even-aged forest, is $8424.50, which 
would be the "full" assessed value of the property at that time. 
After cutting, the assessed value should not exceed $500.95, 
and in practice will be nearer $250.00 if land sells for $5.00 
per acre. The average value for the whole period would corre- 
spond closely to $3239.80. 

The tax assessor, under the present plan, bases his increases 
upon market or sale value, and as the value of young timber is 
seldom recognized, this sale value usually equals the value of 
the soil for other purposes, plus the market value of the timber. 
In this way the property escapes the full effect of repeated 
taxation of capital value. 

A comparison of values for the crop used in Table II gives 
the following results. 

TABLE III 

Comparison of Sale Value with Expectation Value of an Even- 
aged Stand, Including both Land and Timber 



Age, years. 


Sale value with 
land at $5.00. 


Expectation value 
with land at $10.02. 


10 
20 

30 
40 

50 


$5- 00 

22.81 

66.14 

113. 91 

173 -49 


$24.83 

40.83 

66.90 

109.36 

178.51 



The expectation value is based in each instance on the value 
of the crop at 50 years (Formula Gi), and on an interest rate of 

* The Economic Problem of Forest Taxation, by Fred Rogers Fairchild, Yale 
Review, February, 1909. See also " The Nature of Capital and Income," by Irving 
Fisher, pp. 249-255. 



FOREST TAXATION IS7 

5 per cent. Basing the taxes on sale value and revaluing every 
lo years, the total cash taxes paid during the 50-year period 
amount to $43.57 per acre, which is slightly less than the amount 
paid on forests B or C for the same period and over four times 
as large as the sum paid by forest A , which is taxed solely on 
the value of soil. 

Adding compound interest to these annual taxes (Formula 
Ilia), the total tax, with interest, amounts in 50 years to $86.53, 
equalling 51.3 per cent of gross stumpage value, or 53.4 per cent 
of net cash profit on stumpage. But basing the net value of 
the stumpage on the margin over costs with interest or $104.86, 
we find taxes and interest absorbing 82.5 per cent of this margin. 

These taxes are computed as follows: 
Let e = annual tax on original assessed value. 

e' = annual tax on revaluation at 20 years. 

e" = annual tax on revaluation at 30 years. 

e'" = annual tax on revaluation at 40 years. 

e e' e" e'" 
Then E, E' ,E" ,E"' = -^^ -^' -^' -^— • 

o.op o.op o.op o.op 

Sum of taxes (Formula Ilia), 

[\iE'i.op'-''-E-{-E')i.op"'-E"-^E"'\i.op'°-E"-{-E''']i.op''-E"\ 
$5.00 X 0.02 = $0.10, annual taxes for 20 years. 

-^ = $2.oo(£). 
0.05 

$2.00 X 2.6533 ~ $2.00 = $3.30, taxes at 20th year. 
$22.^1 X 0.02 = $0.45, annual taxes for next 10 years. 

— ^ = $9.12 (£') (discrepancy due to decimal values, omitted 
0.05 

in text) . 
$(3-30 + 9.12) 1.6289 ~ $9-12 = $11.12, taxes at 30th year. 
.14 X 0.02 = $1.32, annual taxes for next 10 years. 

^^ = $26.45 (£"). 
0.05 

[11. 12 4- 26.45) 1-6289 ~ $26.45 = $34-76, taxes at 40th year. 



158 FOREST VALUATION 

$113.91 X 0.02 = $2.37, annual taxes for last 10 years. 

'-^ = $47.56 {E'"). 
0.05 

$(34.76 + 47.56) 1.6289 — $47.56 = $86.53, taxes at 50th year. 

165. Effect of the General Property Tax on Forest Production. 

— The effect upon the owner's profits of the system of taxing 
sale value annually depends upon the length of time the present 
owner has held the property, the purchase price, the amount 
of back taxes already paid and the period which must elapse 
previous to cutting. The relation of taxes to the value of the 
property, regardless of ownership, is independent of the purchase 
price or of back taxes, and deals only with the future. A rapid 
rise in prices for timber products so enhances the value of stand- 
ing timber as well as of forest soil that taxes previously paid, 
on very low values, do not absorb an unfair percentage of pres- 
ent value. Whatever over-taxation would have occurred with 
stationary values has been offset by reason of this increase in 
capital value of the property. A continuous increase in value 
of forest property at the same rate as in the past would continue 
to absorb a large portion of the over-taxation due to reassess- 
ments based on sale value. But it does not absorb the compound 
interest item which accumulates on past taxes in absence of 
income from sales. 

Should the owner have paid practically no taxes up to the 
present year, he can pay annually on full value for a definite 
period before the amount of his tax with interest becomes 
equivalent to the taxes paid on forest A. Should he cut his 
timber sooner, he pays less than this tax. For every year which 
the timber stands beyond this period, the tax becomes propor- 
tionally greater than its just equivalent. 

Assuming that the tax of $41.97, the total paid in 50 years on 
forest A, is just, how long can an owner permit his timber to 
stand before incurring over-taxation. The sum of annual taxes 
with interest must equal $41.97. 

E{i.op' - i) = 41.97. 

Omitting all consideration of back taxes, the results are as follows: 



FOREST TAXATION 



TABLE IV 



159 



Periods within which Property Tax on Timber becomes Equivalent 
TO Tax on Soil Value 



Age of 
timber at 
present. 


Present value. 


Annual tax 
2 per cent of 
present value. 


Tax capitalized 


41.97 -T- E, or 

I.Of>^ — I. 


Period indi- 
cated. 


Years 
50 
40 

30 
20 


Dollars 

17349 

113. 91 

66.50 

22.81 


Dollars 
3-47 
2.28 

1-33 
0.46 


Dollars 

69.40 

45 56 

26.60 

9. 12 


. 6048 
0.9212 
I 576 
4.600 


Years 

9 to 10 

13 to 14 

19 to 20 

35 to 36 



The indicated period is found by looking up the factor i.op" 
in the table of values for 5 per cent (Table VI) . The value cor- 
responding to the factor is found opposite the year indicating 
length of period. 

In the owner's mind these periods will be lengthened if he 
bases his standard of value on the capital value of the forest 
rather than on the soil, and would be shortened in proportion to 
the back taxes which he has paid. Increasing prices for forest 
products would lengthen the period, and future increases in the 
assessed value of the property would shorten it. But at some 
future date, not very far distant for mature timber when taxed 
at full value, the timber must be cut or the process of confisca- 
tion begins. After the year in which the accumulating cost of 
annual taxes equals the equitable proportion of value available 
for taxation, the tax steadily confiscates an increasing per cent 
of the capital value. 

With the tax of 2 per cent on soil value, the per cent of "net" 
income appropriated was shown to be 40 per cent. This in effect 
appropriates 40 per cent of 5^, so that for forest land worth 
$10.00 the owner's equity amounts to but $6.00, and the state 
has taken $4.00 in value for taxing purposes. 

But with assessed value increased at lo-year periods the per 
cent of the net future income taken for taxes is 82.5 per cent. 
Since this net income is the basis of capital value of soil, the 
state thus appropriates $8.25 in land value, leaving the owner 
a residual value of $1.75 exclusive of the sum required to reim- 
burse his costs and taxes with interest at 5 per cent. But if he 



l6o FOREST VALUATION 

has paid $5.00 for this land he cannot afford to give the state 
in taxes two-thirds of this cost price as well as his entire net 
profit over 5 per cent. Such a method of taxation therefore 
tends to prevent the private owner from undertaking the business 
of forest production. 

Upon mature timber the effect is to stimulate cutting in order 
to save taxes, whether or not over-taxation has already occurred. 
Few owners stop to compute how much taxes timber should bear. 
They know that the way to escape paying any more taxes is to 
cut the timber. If this is the purpose of the tax it accomplishes 
its object thoroughly, and is a great stimulus to over-produc- 
tion of timber. The only incentive to hold mature stumpage 
under this system is the hope that increased prices will offset 
the taxes. The injurious effects of a bad tax system are not 
reflected fully by depression of values (§ 153), since the resulting 
losses are pocketed by the owners as past costs, and values for 
stumpage continue to reflect only future elements of cost and 
profit. But upon the business of lumbering, in a region of 
large surplus supplies of stumpage, the effect is disastrous, forc- 
ing the weaker operators into bankruptcy and stimulating rapid 
and wasteful cutting on the part of even the strongest holders. 

166. Tax Reform for Forest Property. — From the analysis 
of the financial relation of taxes to values, the most serious flaws 
in the system of taxing forests on their sale value appear to be: 

1. Actual over- taxation through taxing annually the value of 
the entire property including timber, during periods when no 
income is produced, resulting ultimately in confiscation of an 
inequitably large proportion of ultimate or total income. 

2. Uncertainty as to the extent of this over- taxation through 
the arbitrary power vested in local assessors to raise valuations 
at any time. 

Tax reform must remove these two obstacles by substituting 
some system of scientific taxation which will secure equality 
between forest taxes and those imposed on other property when 
gauged by the per cent of income taken, and thus remove the 
element of uncertainty which is even worse than the over-taxation 
itself. 



FOREST TAXATION 1 6 1 

But in effecting this reform the annual local revenues from 
taxation must be maintained. Reduced revenue at present, 
even if made up in later years, causes heavier taxation of other 
forms of property (§ 153). This is the explanation of the failure 
of many attempts to encourage forestry by granting tax rebates 
and exemptions, a form of privilege quickly resented and ren- 
dered ineffectual by assessors through the simple device of 
increasing the assessed valuation of other property belonging 
to the beneficiary. From the facts discussed in Article 161 it 
appears that tax reform must of necessity look to the future 
rather than attempt to correct past errors. On this basis, the 
problem divides itself into: 

The taxation of forest land not containing merchantable 

trees. 
The taxation of land bearing merchantable timber. 

The efforts to secure an equitable tax on forest land devoid 
of merchantable timber are best directed, at present, along the 
lines discussed in Article 163. A combined land and products 
tax best meets the needs of the situation and is most easily 
understood. It must not be forgotten that the products tax is 
justified only when land is not taxed at its full value, and to the 
extent of the margin of accumulated value remaining untaxed. 

Efforts to secure this result have recently been made by several 
states in the northeast. Connecticut permits no increase in 
assessed value of land for fifty years and Hmits the tax rate to 
10 mills. An additional income tax of 10 per cent is then assessed 
on the stumpage value of wood products when harvested. 
Massachusetts permits the revaluation of land exclusive of timber 
at any time so that it is probable that the assessed value will 
be raised to correspond closely with expectation value of the 
bare soil. Taxes are paid annually at local rates. An income 
tax is then levied on forest products at 6 per cent of the stump- 
age value. This tax is equitable only in case the assessed value 
of land will average lower than expectation value, to an extent 
sufhcient to make up the difference represented by the tax on 
stumpage. 

Pennsylvania arbitrarily fixes the value of land at $1.00 per 



1 62 FOREST VALUATIONS 

acre. The state then pays local taxes at 2 per cent of this valu- 
ation, thus assuming the burden of annual taxation for the joint 
benefit of the owner and community. These taxes are never 
refunded by the owner. The owner pays a 10 per cent stumpage 
tax when timber is cut. 

In all these laws only land voluntarily offered by the owner 
and approved by the state forester, or in Massachusetts by 
the local assessors, for classification, comes within the operation 
of the law. This will result in a very gradual appHcation of 
the system. 

No valid objection can be urged to the adoption of similar 
measures in any region, for they do not reduce the present taxes 
and will -result in greatly increased revenue in the future by 
bringing into productive use forest lands which may otherwise 
remain waste. 

The future taxation of lands bearing merchantable timber 
is not so easily provided for. The immediate substitution of 
an income tax which takes the same proportion of income as 
the existing capital tax does of value, is entirely impractical, 
owing to the condition of the capital (§156), Not only would 
the annual taxes from a given forest vary from the former 
amounts paid annually, being either greater or less according 
to rapidity of logging, but this variation would be general; and 
regions where logging is being actively conducted would be in 
receipt of largely increased temporary revenue, while districts 
as yet untouched would be entirely without income from timber 
values. Under the general property tax the local revenue is 
secured only as long as the timber remains standing, after which 
the land alone may be taxed. The loss of current revenue after 
cutting is inevitable under any system. 

A plan proposed * for securing equality of revenue between 
counties, for conditions prevalent in regions of heavy virgin 
stands and large operations, contemplates the postponement 
of the annual taxes on timber until the timber is cut, when they 
will be paid in one sum but without compound interest. To 

* Report of Forestry Committee, 5th Conservation Congress, November, 
1913, page 128. 



FOREST TAXATION 163 

equalize local revenues the state shall act as banker, collecting 
the tax, advancing funds to counties as yet undeveloped, and 
recouping itself from counties where active logging is in process. 

In eastern states a different plan has been adopted. Logging 
is largely in second growth and scattered, so that the problem of 
equalizing the revenues from income is not urgent. The plan 
is to continue the existing valuation of property containing 
timber of taxable value, but to permit no further increase in 
assessed valuation of this timber. When the timber is cut, 
the property is revalued and thereafter taxed only on the value 
of the land. In Connecticut this protection from increased 
valuation is offset by a slight tax on yield, increasing i per cent 
for each decade, for 50 years, so that the advantage to the owner 
of standing timber is not very great. 

Massachusetts has adopted a plan which is worthy of special 
mention. The land containing merchantable timber may be 
revalued at time of classification and pays a land tax similar 
to non-forested land. This tax is subtracted from the total 
tax paid on the entire property previous to classification. The 
balance is the additional amount of tax which the property 
must continue to pay if local revenues are to be maintained. 
This is termed the commutation tax. The amount of this tax 
cannot be subsequently increased, by reason of increased value. 
The principle is that the timber is exempt from annual taxation, 
yet the property pays this commutation tax to tide over the 
gap between the present year and the receipt of the income tax. 
On cutting, the timber pays a 10 per cent income tax, which 
extinguishes the commutation tax. A particularly valuable pro- 
vision is that as soon as timber having a total value equal to 
that of the stumpage originally assessed, has paid a products 
tax, the timber remaining or the increase resulting from growth 
is freed from annual taxation. The community has in the mean- 
time suffered no loss of local revenue and is in receipt of an 
income tax in lieu of increased taxes on advancing values. 

An additional advantage of this plan is that it permits of the 
consolidation, for taxing purposes, of areas of any size and con- 
dition of timber, with land bare of merchantable timber. The 



1 64 FOREST VALUATION 

amount of the commutation tax is made a lien on the entire 
consolidated tract and extinguished by cutting on any portion 
of it. 

Some such plan of taxation is recommended as possessing 
greater merits than an immediate substitution of income tax 
for capital tax in timbered regions. 

No law providing for proper taxation of forest lands should 
give arbitrary powers to a state official to prescribe or regulate 
the scientific methods to be followed by the owner in growing 
trees. The one condition to be insisted on must be that the 
land, especially that without merchantable timber, shall be 
brought under forest cover composed of useful species, and 
maintained as forest land. Cancellation of classification should 
follow failure of owners to comply with these basic conditions. 

To prevent owners from taking advantage of such laws in 
order to escape taxation on property which they may ultimately 
intend for some other purpose, two precautions are used: the 
limitation imposed by classification of lands suitable for forest 
purposes, and provision for payment of a penalty upon cancel- 
lation of this classification. Connecticut and Vermont prescribe 
that lands above a certain value per acre, not including timber 
values, cannot be classified. Massachusetts, in permitting any 
lands to be classified regardless of value, protects the public 
by permitting revaluations, which is perhaps the better 
plan. 

On cancellation of classification the penalty imposed should 
not exceed the difference saved on taxes by the classification. 
Connecticut determines whether the property at time of cancel- 
lation has increased in value and assesses this increase at one- 
half the average rate of lo mills, or 5 mills per year, multiplied 
by the period of classification. The owner thus pays his back 
taxes (without interest), on the theory that the increase has 
been uniform throughout the period. Massachusetts releases 
the owner by the payment of the products tax on all timber 
standing at the time of cancellation. 

The apparent difficulties of securing the adoption of rational 
tax systems for forest property, not the least of which are the 



FOREST TAXATION 165 

constitutional provisions of many states requiring all property 
to be taxed ''equally" under the general property tax, should 
not discourage efforts at genuine reform. The future practice 
of forestry by private owners must be accompanied by the 
adoption of a reasonable and adequate system of taxation for 
forest property. 



CHAPTER XI 

STUMPAGE VALUES 

167. Definition of Stumpage Value. — Stumpage value is 
the sale value of merchantable standing timber — its value on 
the stump previous to felHng and removal. The term " mer- 
chantable " is not so easily defined. Timber is merchantable 
when it is of sufficient size to furnish wood products suitable 
for definite commercial purposes. There can be no fixed 
standard of sizes to coincide with the general definition of 
" merchantable " timber. Trees merchantable for cordwood or 
paper pulp are not large enough to yield saw timber. It follows 
that stumpage value is the sale value of timber intended for 
certain specific uses. The industry which can pay the most 
for the timber determines its stumpage value. In the form of 
stumpage, timber is a portion of the real estate (§§ 134 to 136). 
When purchased with land it may be held indefinitely, but when 
bought or sold separately it must usually be removed within a 
stipulated period. The value of stumpage is ordinarily sepa- 
rated from that of the land, even when both are purchased, 
though in the past the land was often considered of no value 
except for the timber. 

168. Sale Value of Stumpage. — Small bodies of timber, such 
as woodlots, are frequently sold for a lump sum. The value of 
the timber is thus agreed upon without determining its price 
per unit, which is known only to the purchaser after he has cut 
the timber. Areas of considerable size may be sold on the 
basis of a price per acre. 

This crude method is giving place, for large tracts or timber 
aggregating considerable value, to the determination of quantity 
and agreement upon a price per unit, thus arriving at total 
value. But neither quantity nor price are easily ascertained 

166 



STUMPAGE VALUES 1 67 

for standing timber. Products already harvested and measured, 
like wheat or coal, resemble logs or lumber, but the standing 
trees are like the grain before the harvest, or the coal yet in 
the mine; yet not quite the same, for the trees can all be seen, 
and their contents, quahty and value ascertained with some 
definiteness. This requires agreement upon a unit of measure- 
ment for the product, as, for instance, board feet by a given 
log rule, cords or posts. The methods of determining the 
quantity of stumpage are discussed in Chapter XIV. 

169. Stumpage Prices. — Prices for stumpage are deter- 
mined by actual sales, whenever a price per unit of product is 
quoted. But the price obtained for one body of stumpage is 
seldom a safe basis for appraising the value of another stand. 
For no other product is there such need of checking sale values 
by a careful appraisals as for timber stumpage. Practically 
every body of timber should have a separate price, determined 
by the factors which are pecuhar to the stand in question. 
Standard or uniform prices are often established in a region, 
for small bodies of stumpage bought by a single company, 
but this uniformity is usually explained by the fact that the 
purchaser is in position to dictate the price, and could, if he 
wished, pay more for the better lots. 

170. Factors Determining Stumpage Prices. — The value of 
stumpage is derived directly from that of the finished products 
into which it is finally manufactured (§9). The stages in this 
process, in reverse order, are: 

Income from 

retail lumber 

Cost of retail business 

Retailers profits 

Freight charges 

Cost of lumber ) ^ , , ^ .„. 

, , .„ \ = Income from manufacture or muhng = 
f.o.b. mills ) 

Cost of manufacture 
Milling profits 

Per unit of product 

Overrun 
Cost for logs at mill = Income from logging = 



l68 FOREST VALUATION 



Cost of transportation 
Cost of felling and skidding 
Logging profits 

= Income from timberlands, or 



Cost of stumpage < „^ , 

) btumpage value = 

Cost of production, or carrying charges 
Profits 

It is evident that the gross income at any stage in this eco- 
nomic series just equals the total costs plus profits incident to 
the entire chain of processes underlying this income and pre- 
ceding it in point of time, and that the profits, or losses, are 
the factors which balance the successive equations. Stumpage 
value is equivalent to cost of purchase, and tends to increase 
by higher prices for lumber, and to decrease by higher costs or 
by larger profits in retailing, manufacture or logging. 

There may be a great difference between what is paid for 
stumpage and what should be paid. This difference is added 
to the profit of the logger or lumberman (§ i68). 

But actual values for stumpage, as established by sales of 
merchantable timber, do not fluctuate with the annual changes 
in lumber prices. Increased prices for lumber are not imme- 
diately followed by similar increases in stumpage prices, nor 
do the depressions in price, which are so characteristic of the 
lumber trade, make themselves felt at once in a lowered price 
for stumpage. Stumpage prices are sluggish rather than sen- 
sitive. 

Three factors serve to explain this apparent failure of stump- 
age to behave as indicated by the economic relations set forth 
above. The first is the human element in price making (§§ 5-7). 
At best, it takes an expert thoroughly familiar with the costs and 
reasonable profits of such technical and diversified industries as 
logging and milling to determine the proper relations between 
prices f.o.b. at mill for lumber and prices for stumpage. The 
purchaser possesses this knowledge but the stumpage owner 
may not have it. Since it is to the purchaser's interest to keep 
the owner in ignorance, prices are allowed to remain as long as 
possible at the level set by previous sales. This condition is 
disturbed only when competition between two purchasers brings 



STUMPAGE VALUES 169 

prices up to their proper level to the benefit of the stumpage 
owners. The same condition is secured when timber is 
sold by a lumber company which is fully acquainted with its 
value. 

The second factor is the controlling influence of transportation 
and logging costs. Logging alone frequently requires a large 
investment in railroads, flumes and equipment. It is often im- 
possible for the owner of a small body of timber to market it, 
except by means of the facilities owned by a lumber company. 
The owner feels entitled to the stumpage value which results 
from these increased transportation facilities. The lumberman 
endeavors to secure the stumpage at the value which it had 
before his improvements were constructed. When he is the 
only purchaser, his price, rather than that desired by the 
owners, is usually determined upon as the value of the 
stumpage. 

The third factor is the element of time. Present prices of 
finished lumber can under no circumstances determine present 
stumpage prices absolutely. In the first place they do not 
apply to present but to past stumpage values, and the value of 
present stumpage will depend upon the price obtained when 
its product, in turn, reaches the market (§ 11). 

But the period required to bring the timber from the stump 
to the retailer, or even to the cars, is not the most important 
element of time involved, and neither the discount factor nor 
the speculative probability of a change in value for this short 
period would have much influence on stumpage prices. A 
more important fact is that large bodies of stumpage cannot 
be logged at one time. The operation must extend over several 
years. Therefore the prices finally received for this lumber will 
not be this year's or next year's prices, but an average of many 
years. Averages tend to eliminate annual fluctuations. Stump- 
age values do not fall when lumber prices decline because the 
owners of stumpage expect that before they have finished cutting, 
these lumber prices will have risen again. 

171. Appraisals of Stumpage Value. — ' An appraisal of 
stumpage value requires: 



I70 FOREST VALUATION 

(a) Acceptance of a definite class of products or stage of 
manufacture as furnishing a basis of prices from which to under- 
take the appraisal. The further removed this basis is from 
stumpage value, the greater will be the difficulty of correctly 
appraising the intervening elements of cost and profit. But 
the more stable and widely accepted are the prices which fur- 
nish this basis, the more reliable will be the result. 

(b) Appraisal of expenses of the intervening operations as 
logging, or logging and milling, including depreciation of capital 
assets employed in these enterprises. 

(c) Determination of legitimate profits for logging and mill- 
ing, and of the proper basis and method of computing what 
such profits should be. 

(d) Residual or stumpage value after subtracting elements 
b and c from a, and correcting for the error caused by 
overrun, in order to express value of stumpage in terms of 
log scale. 

172. The Price Basis in Appraisals. — The acceptance of the 
retailer's price as the starting point for appraising stumpage 
values would interpose retail costs and profits as an element 
in the appraisal. This would result in appraising the value 
of lumber f.o.b. cars at mill, instead of accepting the current 
prices already determined for this lumber by sales; such a course 
is obviously undesirable. 

Were the prices of logs standardized, and determined in open 
competitive market as are wholesale lumber prices, there would 
be a similar argument for accepting log prices instead of sub- 
stituting an appraisal of the value of logs. This method has 
been used on Puget Sound where such a log market exists. 
Whenever logging is conducted as a separate business, and not 
merely by contract for the manufacturer, the price of logs does 
determine what may be paid for stumpage, and must be taken 
as the basis of appraisals. 

It is claimed that in markets established for logs, prices for 
the logs are not as high as an equitable appraisal would indicate 
owing to the ability of the mill owners to keep these prices 
under control. Where the log market is the only outlet for the 



STUMPAGE VALUES 17 1 

logs, this fact would not justify an appraisal of stumpage based 
on higher log prices, unobtainable in practice, although it might 
justify holding rather than selling the timber. 

But in the majority of cases, the business of logging is either 
conducted by the same firms which manufacture the timber, 
or the manufacturer purchases the stumpage, contracts the log- 
ging and thus bases the price which he can pay for the stumpage 
on the price of lumber at the mill. Stumpage appraisals must 
thus conform strictly to the prevalent economic conditions, and 
must be based on the value of the product put forth by the 
operator who purchases the timber, provided he conforms to 
general customs in the locaHty. 

Mill prices for lumber fluctuate not only with the season 
and condition of the market, but are affected by freight charges. 
In certain locaHties, prices at large central markets for lumber 
may be taken as standard, and the proper discounts made for 
local freight rates. 

The main source of variation in mill prices Hes in the variety 
of products, and of grades of the same product, into which the 
timber is manufactured. This difference exists originally in 
the quality of the trees or logs, and is increased by the methods 
of handling the raw material or logs by the millman. One mill 
may, from the same material, produce a much greater per cent 
of the more valuable grades than another, whose principal out- 
put m.ay be dimension lumber. 

These differences in the quality of the grades produced vitally 
affect stumpage value and give to old timber a value at present 
prices which second growth timber may never obtain in the 
future because of inferior quality. 

Two plans may be used in obtaining a price basis for the 
appraisal of a given body of stumpage. The first, advocated 
by the U. S. Forest Service in Washington and Oregon, is based 
on grade prices at a central market, discounted for freight 
rates to the required locality. 

The first step is to estimate in the field the per cent of each 
of certain standard grades which will probably be yielded by 
the body of timber to be appraised. The average price of each 



172 FOREST VALUATION 

grade is obtained and a per cent of this price taken equal to the 
per cent of the total stand represented by the given grade. 
These fractional prices, when totalled, give an average price 
weighted both by quantity and value for the grades ex- 
pected.* 

The second plan depends upon "mill run" prices. In the 
absence of stable central markets, average prices for the total 
output of mills, termed mill run prices, are advocated. This 
method is defective for several reasons. The higher the average 
prices for lumber, the more profitable it becomes to manufacture 
low grades. In periods of depression these grades may be left 
to waste in the woods. An increased output of cheap grades, 
which always follows higher prices, may actually lower rather 
than raise the average mill run prices for lumber. Again, when 
prices are based on average mill run, the per cent of grades 
sawed may not coincide with those which can be produced from 
the timber to be appraised, either because the mill may have 
been cutting in timber better or poorer than the average, or, 
because the timber to be appraised may be better or poorer 
than the average. Mill run prices for timber known to be of 

* The following figures, used in determining the average price of lumber in con- 
nection with a recent timber sale in Washington, were furnished by Asst. District 
Forester, F. E. Ames, U. S. Forest Service, and serve to illustrate this method. 

Douglas Fir Grades, Prices and Average Value 

No. I V. G. Flooring 3% @ $26.00 $0.78 

No. 2 V. G. Flooring 5% @ 23.00 1.15 

No. 2 and Bet. F. G. Flooring 3% @ 15.00 .45 

No. 2 Clear and Bet. Finish 5% @ 26.00 1.30 

No. 2 Clear and Bet. Siding and Rustic. . 4% @ 17.00 .68 

No. 3 Clear Flooring. Siding and Rustic 8% @, 13.50 1.08 

No. I Shop 4% @ 16.00 .64 

Car Sills 6% @ 16.50 .99 

Timbers 15% @ ^°-3° i-5S 

Dimension 28% @ 9.10 2.55 

Boards and Shiplap 12% @ 8.75 1.05 

Dunnage 7% @ 6.00 .42 

$12.64 

The grade prices represent the average of the quarterly averages from July i, 
1911 to July I, 1914. Underweights not included. 



STUMPAGE VALUES 1 73 

similar quality to that appraised removes this objection. Aver- 
age mill run prices for several mills in a region are serviceable 
only when the timber is remarkably uniform in quality and 
grade. 

173. Depreciation. — Depreciation plays so much more im- 
portant a part in stumpage appraisals than in forest pro- 
duction that it should be given special consideration in this 
chapter. 

Depreciation is a sum written off or subtracted from the cost 
of capital assets, to correspond roughly or approximately with 
a shrinkage or disappearance of value through diminishing use- 
fulness. An investment in a fixed or durable asset is not an 
"expense " at the time of purchase, but an exchange of cash for 
another form of property. The real expense is incidental to 
the use or service which this property yields, by reason of which 
it diminishes in value. Depreciation on property for which 
there exists a continuous need corresponds to actual deteri- 
oration and final discarding of the article as worn out. But 
where the period and amount of use is limited and the property 
will outlast its usefulness, the residual value will coincide with 
the value of the material of which it is composed, for removal 
or use in some other line. This shrinkage in value not accom- 
panied by physical deterioration may be termed "amortiza- 
tion." 

When depreciation is added to other expenses, the sum gives 
the total actual outlay or cost of the business, in which total 
the investment in capital assets subject to depreciation is ex- 
cluded, as not constituting a cost. 

A depreciation fund is a fund created by the setting aside 
annually, from net income, amounts intended to eventually 
equal the total depreciation (§ 73). When the period is known 
with reasonable certainty, the amounts annually needed to 
accomplish this purpose can be computed in advance. 

Let A = original capital investment. 

W = final or wrecking value. 
D = total depreciation or A — W. 
n = years in period. 



174 FOREST VALUATION 

Four methods may be used in determining depreciation. 

Method A. The total depreciation may be refunded by de- 
positing each year in a savings bank, at p per cent, or investing 
and reinvesting, annual sums in such a way as to earn compound 
interest, so that the total of principal and interest at the end 
of the period equals the depreciation. This fund is not returned 
to the owners until the expiration of the period. Their capital 
investment remains at its original figure, and the annual divi- 
dends are declared on this basis. 

Let X = annual sum for depreciation. 

Then _^(i.o/>"- i) = D, (See III.) 

o.op 

^ ^ D (o.op) _ ,p. 

I.O^" — I 

This method is seldom, if ever, employed in connection with 
annual business, although it is practical as the basis of a sinking 
fund for the payment of bonds. 

The other three methods neglect the factor of compound 
interest on the annual payments, and undertake to repay, 
through a series of years, sums whose cash total will just equal 
the total depreciation. 

Method B. This method proposes to pay the total depre- 
ciation in equal annual instalments covering the requisite 
period. The formula is 

^ D A-W .ps 

X = — or • (Fi) 

n n 

The method is used more widely than any other and is easily 
understood and applied. Actual return to investors of this 
annual appropriation for depreciation would have the result of 
diminishing the capital investment annually. 

Method C. Instead of depreciating the capital by equal 
amounts annually, the depreciation may be made to equal a 
fixed per cent annually of the residual value of the capital; 
its value less previous depreciation. By this means, depre- 



STUMP AGE VALUES 175 

ciation expense is heaviest in the earlier years, and steadily 
diminishes. 

Let z = per cent of depreciation, and 

o.oz = per cent expressed decimally. 

Then ^(i -o.oz)" = W, 



0.02 = I -\7y, 



{-N?!) 



z = 100(1 -\/'^y (P2) 

This method is seldom employed as it is inconvenient to write 
off large sums for depreciation in the earlier stages of the business, 
especially in lumbering. 

Method D. This method proposes to increase the amount 
charged to depreciation annually, and combine it with an annual 
interest return on the diminished or residual capital, in such 
amounts that the sum of interest and depreciation will require 
equal annual payments. Depreciation, by reducing the invested 
capital, correspondingly lowers the interest returns required 
by a given rate of interest. This reduction in interest may be 
added annually to depreciation. It only remains to determine 
what annual sum in excess of interest on the original investment 
is required for the first payment, to secure this balance between 
the two elements of interest and depreciation, so that the 
sum of the increasing payments on account of depreciation will 
at the close of the period just equal the total amount to be 
written off. 

In this case, either of two solutions is possible to determine the 
annual payment. 

Let Z = annual payment for interest and depreciation. 

I o/'" — I 

Let d = ^-^ , when p = rate of interest to be earned on 

o.op ' ^ 

capital A. 



176 FOREST VALUATION 

Then Z= Ail^q^w; (p,) 

a 

or Z = Aio.op)+^-^ (P4) 

a 

The first formula utilizes the wrecking value, while the 
second introduces total depreciation, and is somewhat simpler. 
The factor d is easily computed from Table VI, or, for values of 
p not given, by logarithms, in which the logarithm of i.op is 
multiplied by n to obtain the logarithm of i.o/>"4 

* "Modem Accounting," by Henry Rand Hatfield, page 132. 

\ {A • I.op — X) I.op — X] I.op ... to w terms = W. 
A (r.o^") - X{i +i.op + 1.0^2 _ _ , i.o;>"-i) = W. 

A (i.o/>") - X ^""^^ ~ ^ = W (by Formula Qi). 
I.op — I 

A (i.o/'") - W 

J^ — „ 

I.op"— I 
op 

^ A (i.op'') - W 
d 
t Proposed by W. B. Hunter, formerly special examiner in U. S. Bureau of 
Corporations. 

Let X = A (o.op) + e. 

Then, in second year, 

{A ' o.op — e) o.op = interest on capital. 
e (o.op) = increase in depreciation, 
e + e (o.op) = e (i.op) = depreciation. 
In third year, 

(A • o.op — e • I.op) o.op = interest. 

e (i.op) X o.op = increase in depreciation. 

e (i.op) — e (i.op) X o.op = e (i.op^), depreciation. 

D = e+e (i.op) + e (i.op'^) . . . i.o/>"-i 

o.op 

I.op" - I , 

■ = a. 

o.op 

e = X — A (o.op). 
D = (X -A' o.op) d. 

X = A (o.op) +-■ 

t The objections urged against this method are : first, that it allows interest on 
invested capital as a cost (Hatfield); second, that a plant depreciates more rap- 
idly during the first few years than thereafter, and loss during that time would 



STUMP AGE VALUES 1 77 

174. Milling Costs and Profits. — The cost of milling or 
manufacture may be standardized for operations of a given 
size. The current expenses, or operating costs, do not vary 
greatly. For operations involving a definite quantity of stump- 
age, the duration of the operation is largely determined by the 
capacity of the mill. 

The factor which indicates the most profitable size for a mill 
is the relation between the depreciation of fixed costs or capital 
expenditures for the plant and machinery, and the period and 
quantity of output over which this cost must be distributed. 
The value of the mill when there is no more timber to cut is 
practically nothing, and that of second-hand machinery, very 
small. The difference between these final values and initial 
cost, which represents depreciation, is one of the principal 
elements of expense (§ 173). 

The size of this item of depreciation and the relation which it 
bears to the total output, and to the total cost of producing 
each unit of product, evidently depends more upon the total 
length of time over which the plant can continue to operate 
than upon its daily capacity. With mills of equal efficiency, 
the one with a twenty-year cut may be considered as having 
about half the depreciation expense per unit of output that one 
with but ten years' cut must write off. 

Provided the supply of logs is assured, and the period over 
which to distribute the cost of depreciation can be approxi- 
mated, the requisite profits in manufacturing may be gauged 
with reasonable uniformity. Uncertainty as to future timber 
supply makes it necessary to guard against a shortage or com- 
plete exhaustion of raw material by a correspondingly large 
appropriation from gross income for depreciation. Should 
this shortage not materialize, the concern would later find its 

find the proprietors without adequate provision for meeting this loss. The first 
objection does not apply when the purpose of the computation is to determine 
profits in advance, since these are not treated as costs. The second objection 
holds good if it is considered necessary to make the amounts written off for de- 
preciation agree closely with actual loss in value. The results obtained by 
this method agree more closely with those of Method A than with Method 
Bor C. 



178 FOREST VALUATION 

financial position and average profits correspondingly, and justly, 
increased by these earlier sacrifices. 

The costs and profits of manufacture are both included in 
contract prices for sawing or manufacturing products, which 
is the basis of operations of many portable saw mills. 

175. Logging Costs and Profits. — It is in the logging, rather 
than the milHng end of lumbering, that the greatest variations 
in costs occur. The cost of felling and bucking the trees into 
logs, ties or poles may be standardized. But the cost of trans- 
portation of the product from the site to the mill is determined 
by a number of exceedingly variable factors, and is the prin- 
cipal part of logging. 

These factors are: accessibility and quantity of stumpage, 
and methods of transportation adapted to climate, to the topog- 
raphy and to the size of the timber. The direct relation of total 
quantity or volume upon the cost per unit of the combined 
expense of constructing the transportation routes and moving 
the product needs to be emphasized (§ 98) , and explains the 
great differences in value of timber of equal quality but differing 
merely in quantity available. 

Accessibihty is a relative condition depending upon the total 
cost per unit of product to bring the timber to the mill, and the 
margin of profit remaining for distribution between the owner 
of stumpage and the logger. When the logger sees so small a 
margin that he demands it all, the timber is for the present 
inaccessible. Accessibility depends, then, upon the total volume 
available as well as upon the location of the site and the diffi- 
culties and costs of transportation intervenmg between site and 
mill. 

Methods of transportation exercise a profound influence 
upon logging costs. The factor of climate exerts its chief influ- 
ence upon the bottom, making ice roads possible in some regions, 
while in others rain greatly increases the difficulties by soften- 
ing the soil. The driving of streams, supplemented by the 
sleigh haul, may be superseded by rail transportation involving 
an investment of an entirely different character. For short 
distances, in regions of second growth, wagon haul is the chief 



STUMPAGE VALUES 1 79 

dependence of the operator. The overhead cable to supple- 
ment the railroad may prove cheapest, as in cypress swamps or 
over broken gorges, while elsewhere, skidding by ground cables 
or with animals is most efficient. 

In appraisals, average logging costs for the specific body of 
timber, based on the methods accepted by experience in that 
region as best and cheapest, will be the basis of costs. Excessive 
costs due to deliberate use of methods shown to be antiquated 
or expensive, when the operator is in position to use better 
methods, or when others can be found who will do so, cannot 
be permitted to influence or increase the factor of logging costs. 
An additional cost is incurred in logging under forestry prin- 
ciples (§§ 107 and 176). 

The profits in logging are less easily gauged than in milling. 
The great variation in conditions, which makes each logging job 
or ''chance" a separate venture, prevents the standardization 
of methods and increases the uncertainty of the total estimated 
cost, and consequently of the risk of loss. Added to this is 
the risk from natural agencies, as floods, fire, drought, lack of 
cold weather, too much snow or any other variation from normal 
which either directly damages the timber or the means of trans- 
portation, or unduly increases the labor and cost of logging. 

Logging work is less closely supervised from the main office 
than is milling. Hence woods bosses are more largely thrown 
on their own resources. The main attributes of woods foremen 
even now is brute force and practical experience. This type 
of boss lacks ability to apply methods of scientific efficiency. 
The average risk in logging is probably double that incurred 
in manufacture. 

Depreciation as an item of expense in logging chiefly concerns 
the means of transportation. The entire initial cost for tempo- 
rary railroads, flumes or roads, which will be abandoned on com- 
pletion of the operation, is depreciated or charged off as a cost 
of logging. The costs for railroads, or roads which will after- 
wards be used for permanent traffic, will be maintenance and 
the difference in value of the road at the beginning and end 
of the operation. A logging company which subsequently sells 



l8o FOREST VALUATION 

the road to a railroad company for continuous operation may 
secure a price equal to the cost of the road, in which case no 
depreciation is incurred. Such a result cannot be assumed, and 
depreciation must always be charged against the transportation 
system. 

The cost of all logging equipment, such as cables, engines, 
horses, and other supplies, should be reckoned not in the form 
of a capital expenditure but as depreciation. 

176. Stumpage as a Capital Investment and as a Cost of Raw 
Materials. — Methods of appraising the value of stumpage on 
the basis of the present net residue, after subtracting logging 
and manufacturing costs and profits, are based on the supposi- 
tion that this timber will be removed within a short time, not 
exceeding three to five years. Such values are applicable to 
short-term contracts or to small bodies of timber, and to pur- 
chases in which land is not included. But the purchase for 
cash of large bodies of stumpage introduces an additional ele- 
ment of cost which must be considered by the purchaser. The 
time which must elapse previous to the actual completion of 
cutting necessitates the holding of this stumpage, with accom- 
panying annual expenses (§ 170). This would apparently lower 
the price the purchaser can pay, in the same manner that the 
absence of a market at present, even if it is sure to develop 
later, depresses present values. When transportation facilities, 
mills and markets are ready, the price will be correspondingly 
higher than in regions where development must follow purchase. 

It is not possible, however, to arrive at a proper appraised 
value for large areas of standing timber by the method of com- 
puting the value for immediate cutting, and then discounting 
this value for the average period which the timber must 
stand. 

In spite of the impossibility of immediate cutting, the timber 
will usually sell for the value shown without such discount. 
This is explained by the element of increasing prices, to which 
may be added growth of timber and improvement in quality. 
It would be unfair to discount a future stumpage value based 
on present sales, when everyone, purchaser and owner alike, 



STUMPAGE VALUES l8l 

expects stumpage to increase in value (§ i88). Were it definitely 
known that no such increase would occur, the expectation value 
of the revenue from cutting the timber would be less than the/ 
present sale value for immediate cutting. As it is, the expec- 
tation value of the stumpage is based on this probable increase 
and its present sale value is not depressed by the postponement 
of cutting. Again, the great advantages accompanying the 
ownership of large bodies of timber and the reduction of depre- 
ciation costs (§ 173) and transportation charges (§ 174) in them- 
selves more than offset such possible discount in value. ^ 

The value of stumpage for immediate purchase as a capital, 
investment may therefore be appraised on the basis of what 
it is worth on the completion of the necessary transportation 
and milling facilities, or, if these are assured, it may safely be 
based on present value. 

For stumpage which is paid for in small instalments just 
previous to or following the cutting of the timber, the value is 
manifestly that existing at the time of payment. On long-term 
contracts, as a result of such postponed payments, a readjust- 
ment of stumpage values is required at reasonable intervals, 
on account of the expected increase in future prices of lumber. 
This method of payment, by which the operator is relieved not 
only of the investment with its attendant annual expense, but 
also of the risk, and of any losses which may result from fire 
or any other agency, puts stumpage in the same class as that 
of raw materials, rather than capital. The attendant advan- 
tages* to the purchaser, corresponding to the prospective loss 
and risk of holding timber, are recognized as having a value 
great enough to form a material inducement in sales of timber 
on National Forests. It is usually sufficient to offset the addi- 
tional cost of brush burning and other silvicultural measures 
required by the government. 

177. The Determination of Legitimate Profits. Overturn 
Methods. — Costs must be gauged .in relation to the quantity of 
product resulting from a given expenditure, and a cost account 
seeks to determine the cost and the resulting profit on each 
unit (§25). All factors of cost, including depreciation, may be 



l82 FOREST VALUATION 

expressed on the basis of a thousand board feet, cord or other 
unit of product. 

The surplus after subtracting costs from the average price 
of the product is the net profit, from which is paid the returns 
on the invested capital and the enterpriser's gain for services 
(§39). If the cost of stumpage is fixed, this, added to other 
costs, determines the logger's profit. In appraisals of stumpage, 
on the other hand, the net surplus after paying all other expenses 
must be divided between stumpage and profit, and the deter- 
mination of legitimate profit must precede that of stumpage 
value. 

On small ventures, where the enterpriser depends almost en- 
tirely on his individual efforts and the amount of capital invested 
is insignificant, most of the annual costs are met from income, 
depreciation is a small item, and profit is usually gauged by the 
margin of income over costs for each unit. Logging contractors 
are satisfied if they realize, say, $1 profit per thousand board 
feet log scale above their computed expenses. Profits may 
always be expressed in this manner, whether or not the calcula- 
tion stops at this point. This has been termed the overturn 
method of expressing profits, since the working capital used for 
wages and other current expenses is turned over or used once 
for each unit of output. 

The contractor bases his profit on costs of logging, exclusive 
of stumpage. 

Let Lc = logging costs. 

Mc = milling costs. 

D = depreciation costs j ^^'^^Vmm'ing. 

5 = sale value of lumber or of logs. 

P = profit. 
Ym = stumpage value of 1000 board feet of 

manufactured lumber. 
q% = legitimate profit. 

Then P = g%{Lc + D). 

Ym = S-{Lc-^D)- q% {Lc + D). 



STUMPAGE VALUES 183 

That is, if the price for logs is taken as the basis of prices, 
and the logger computes his requisite profit roughly as a per 
cent of average logging costs, stumpage value is the residue 
after subtracting costs and profit from sale prices. 

In the same way, milling costs and profit may be subtracted, 
and (Method A) 

Yr.= S-{Lc^Mc + D)- q% (Lc -\-Mc-\-D). (R) 

Should milling require a different profit from logging, these 
costs and profits may be separated, using r per cent for profit 
in milling. 

Yn, = S -{Mc-{-MD-\-Lc + LD) - r% {Mc + MD) 

-q%{Lc + LD). (Ri) 

The computation of profits as a per cent of operating costs, 
if based on the results of individual operations, would place a 
premium on extravagance. But when gauged by average costs 
of well-conducted operations of similar size, and applied in deter- 
mining appraisals in advance of cutting, no such objection can 
be urged. 

Method B assumes that stumpage is a part of the total 
operating costs, and that the money invested in it is entitled 
to share in the profit. By thus adding stumpage to the sum 
of the other expenses, the total of costs plus profit equals gross 
income, or sale value. Profit thus becomes a fixed per cent 
of this sale value, and is independent of operating costs. Any 
increase in operating expense of logging is subtracted from cost 
of stumpage, and vice versa. 

The formula is: 

F,„ = 5 - {Lc -]-Mc + D) - q7o {Lc + Mc -\- D + FJ, 
which reduces to 

Ym = ^ ^ - {Lc -hMc-\-D). (R2) 

I + g% 

This formula was formerly advocated by the Forest Service 
for use in small sales where but little capital is invested, but has 
been set aside in favor of Method A. The profit q% should be 
exclusive of a salary of $1200 to $1500 for the operator (§34). 



1 84 



FOREST VALUATION 



Md:hod C is to share the profit or margin between the owner 
of stumpage and the operator. Such a plan requires complete 
confidence in the integrity of the operator or a right to inspect 
his books, and is not generally practiced, though one of the most 
equitable of methods. 

It is the only one of the three methods proposed above, 
which can be based on the actual costs of a given operation, 
with safety to both parties. Letting q per cent equal the per 
cent of net income taken for stumpage value, the formula is 

Ym = q%\S- (Lc -^Mc + D)l. (R3) 

In the following diagram the basis and results of these three 
methods is shown, and the effect of an increase of operating 
costs upon profits and stumpage values. 

DIAGRAM III 

Comparison of Costs, Profits and Stumpage Value by Overturn Methods 



Sale Value 17.00 



Method A 



Method B 



Method C 



Costs 11.00 


1 Profit 3.20 1 Stumpage 3.80 


Costs 13.00 


1 Profit 2.60 te'"^° 


Profit 20^ of Costs 


Coats 11.00 


1 Stuiui)ag-e 3.i5 


Profit 2.55 


Costs 13.00 


1 stumpage 
1 1.45 


Profit 2.55 


Profit lb% of Sale Value 


Costs 11.00 


j Profit 3.00 1 Stumpage 3.00 


Costs 13.00 


1 Profit 2.00 1 ""^T,"'^' 



Profit 50:^ of Net Income 



Operating costs, profits and stumpage value based on i M board feet of lumber, 
scaled in the log. 

178. The Investment Basis for Profits. — Although profit 
may be expressed in terms of per cent of cost, or of sale value 
for a unit of product, it can be correctly gauged only as a return 
on invested capital in which is included the enterpriser's gain 
(§§32, 33). The knowledge that a profit of $i per thousand feet 
has been earned does not suffice as a basis for dividends. The 
reward for personal services, which is so large an element in small 
undertakings, disappears with large enterprises, and net income 



STUMPAGE VALUES 185 

or profits must be converted into annual dividends earned on 
invested capital. 

The capital upon which this income is earned is the entire 
amount of fixed and working capital employed in the business, 
including that which is borrowed. It is of no significance that 
working capital is turned over several times in a season, as is 
done in railroad logging, except as it increases the total net 
income which is the product of the profit per thousand feet 
multiplied by the year's output. This income is not the product 
solely of the working capital, but of the total investment. 

Interest on borrowed capital is paid out of this net income, 
and it is immaterial whether the capital entitled to share in 
the income is taken as the entire investment, or as the portion 
owned by the proprietors, excepting that the latter are entitled 
to a larger rate of profit in proportion to the lessening of their per 
cent of total capital and corresponding increase of risk (§32). 
In stumpage appraisals it is advisable to compute the profit on 
the total investment, thus eliminating the purely personal ele- 
ment as to what proportion of the capital is borrowed. 

It must be self-evident that interest is not a "cost" in stump- 
age appraisals, but it may be so regarded without harm, pro- 
vided it is not added to operating costs in Methods A, B and C 
(§ 177)) and is subtracted from income allowed by the investment 
method. To permit profits to be earned on income represented 
by interest on owner's capital, results in serious inflation of 
profits and resultant heavy losses in stumpage values (§42). 

The main difficulty in computing profits in the form of a 
return on the average annual investment arises from the ele- 
ment of depreciation, and its effect in reducing the capital 
invested year by year. 

It is possible to earn annually about the same net surplus, 
available for depreciation and profits. To base the amount 
of these profits upon the maximum investment, which occurs 
normally in the first or earlier years, results in a steadily in- 
creased rate of profit on the capital remaining invested in sub- 
sequent years, and an average rate considerably greater than 
intended, with corresponding loss in stumpage value. 



1 86 FOREST VALUATION 

By the use of either of the formulae given in Article 175, Method 
D (P3, P4), a fixed rate of profit may be found, which will apply 
to the residual capital actually invested annually. This is 
accomphshed through the increasing payments for depreciation. 
The sum of interest and depreciation, or Z, calls for equal income 
annually. This conforms with the financial conditions which can 
normally be secured in lumbering. To the owners, it makes 
very little actual difference whether their annual income is 
termed dividends or depreciation. They expect to allow the 
larger portion of their capital to remain invested throughout 
the Hfe of the enterprise, and this result is accomplished by 
increasing depreciation from small beginnings. Apparently, 
there is no valid objection to the adoption of this method of 
determining the average per cent of profit to be allowed on 
invested capital. 

Should the method of allowing equal annual amounts for 
depreciation be adopted (§175, Method B) the average amount 
of capital invested during the prospective Hfe of the enterprise 
must be determined. The investment for each year is taken 
at the beginning of the year. The average for the period is then 
equal to the residual or final investment (W) plus one-half the 
total depreciation, plus one-half the annual depreciation. For 
an investment of $20,000, with a residual value of $10,000, over 
a period of five years, the values at the beginning of each year are 

First year $20,000 

Second year 18,000 

Third year 16,000 

Fourth year 14,000 

Fifth year 1 2,000 

Average investment $16,000 

which equals 

Residual investment $10,000 

One-half total depreciation 5, 000 

One-half annual depreciation 1,000 

Average investment $16,000 



STUMPAGE VALUES 187 

This amount would be taken as the basis for computing the 
per cent of annual profit to be allowed. 

179. Overrun. — When the amount and per cent of profit 
have been determined, the remainder, or stumpage value, is a 
definite proportion or per cent of the sale value of the manu- 
factured products, and equals a stated price per thousand 
board feet. Should stumpage appraisal indicate a value equal- 
ling 20 per cent of the wholesale price or mill price of lumber 
worth $20 per thousand, the price of stumpage will be $4 per 
thousand feet of sawed lumber. 

But this does not indicate that the true price of stumpage 
is $4. It is probably considerably more. The contents of 
logs, and not the measured products, is the basis of payment, 
not only when the timber is bought on the stump, but when it 
is paid for after being felled and measured. 

Only in case the logs are measured by a rule which will give 
the actual sawed contents, will the appraised stumpage value 
per thousand feet be the same when measured by log scale 
and by sawed contents. All log scales in extensive commercial 
use give less than the contents ordinarily sawed from logs, and 
this discrepancy increases as utilization becomes closer. The 
excess of manufactured lumber over the contents measured by 
the log scale is termed overrun. 

With certain log rules, notably the Doyle and Doyle-Scribner, 
this excess amounts to 25 per cent and over, and increases with 
small timber. 

Should the overrun be 25 per cent, it indicates that for timber 
worth $4 per thousand, each thousand feet log scale produces 
1.25 thousand feet of lumber. The value of the stumpage is 
therefore 1.25 X $4, or $5 per thousand. 
If 

Ym = stumpage value per thousand feet of sawed lumber, 
s = per cent of overrun per thousand feet of log scale, 
Y = resulting stumpage value per thousand feet log scale, 

then 

Y = Y^X i.os. 



1 88 FOREST VALUATION 

180. Stumpage Values for Different Species in Mixed Stands. 
— In a mixed stand containing two or more species, the sale 
value of the products of these species usually differs considerably. 
Often only one valuable species will be removed from a mixed 
stand. As values increase, other species become profitable, and 
finally, all may be taken. 

At a point just before the inferior species become sufficiently 
valuable to be logged, the operator is under the necessity of con- 
structing his transportation system, and incurring his entire 
cost for equipment and overhead expenses, in order to log a 
portion of the stand, thus moving a smaller volume of lumber, 
at relatively greater expense per unit. 

Assuming that the total costs, including depreciation, amount 
to $12 per thousand board feet, and the most valuable species 
is worth $20, the margm for profit and stumpage is $8. A 
species worth but $12 on the market could apparently not be 
marketed at all. But there is very little additional investment 
involved in logging this second species. By doing so, the total 
average cost of logging may be reduced, by lessening the trans- 
portation expense per unit, the average of overhead charges, 
and the depreciation, to $10 per thousand feet for the entire 
operation. This adds a profit of $2 to the more valuable species, 
and leaves a margin of $2 for the inferior one, for profit and 
stumpage. 

But such a cost distribution is unfair to the inferior species, 
since the operation does not depend on its presence and the 
capital expenditures must be incurred without its inclusion. 
It has been suggested that the more valuable species or group 
be made to bear both the entire cost of depreciation, which 
represents the capital expenditures, and the overhead charges. 
The inferior group is left to bear merely its proportion of oper- 
ating costs. This plan is rather crude where there are several 
species, all of different values. 

The following method is quoted verbatim from the Manual 
of Stumpage Appraisals, U. S. Forest Service, November, 1914. 
This plan offers an equitable solution of the problem. 

" The most satisfactory method is to pro-rate the gross annual 



STUMPAGE VALUES 



189 



depreciation and profit over the difference between operating 
cost and selling price, for each species, in the quantities entering 
into the annual cut. 

To illustrate: 

A yearly cut is made up of 4 million feet of sugar pine, 3 mil- 
lion feet of yellow pine, and 2 million feet of white fir (giving a 
total of 9 million feet).* The margins between selling prices and 
costs of production, exclusive of depreciation and profit, are : 



Species. 


Selling price. 


Operating cost. 


Margin. 


Sugar pine 

Yellow pine 

White fir 


$20.00 

18.00 

(16.00) 


$10.00 
10.00- 
(10.00) 


$10.00 
8.00 
6.00 



The total net value, or sum of the margins over which depre- 
ciation and profit may be pro-rated, is thus: 

Sugar pine $10.00 X 4000 M = $40,000 

Yellow pine 8.00 X 3000 M = 24,000 

White fir 6.00 X 2000 M = 12,000 

Total $76,000 

The annual sum of depreciation and profit (investment 
method) which must be paid out of this total has been computed 

as $34,200. Hence -'^T^ = $0.45. That is, every dollar of 

76,000 

margin between operating costs and selling price must pay 

45 cents toward profit and depreciation. Put in quantitative 

terms, by species, we have the following charges per M feet for 

depreciation and profit: 

Sugar pine 10 X $0.45 = $4.50 

Yellow pine 8 X 0.45 = 3.60 

White fir 6 X 0.45 = 2.70 

By this method inferior species which yield no margin between 
operating costs and selling price, or a negative margin, but 
which must be included in the sale for silvicultural reasons, 

* The bracketed material does not appear in the original quotation and has 
been inserted as additional explanation. 



I go FOREST VALUATION 

are automatically relieved of profit and depreciation, and the 
charge upon the other timbers for these items proportionately 
increased. 

The same result is readily obtained on a thousand foot basis, 
using the per cents of the different species in the cut. That 
is, to obtain the average margin (of sale value above operating 
costs), multiply the margin for each species by the per cent of 
this species in total cost: 

45 per cent sugar pine at $10.00 $4.50 

33 per cent yellow pine at $8.00 2.64 

22 per cent white fir at $6.00 1.32 

Total ■ $8.46 

Depreciation and profit per M feet ( -"^ — I $3.80. 

\ 9000 / 

^' - ■ = $.045, to be taken from each dollar of margin for 
8.40 

these items. 

This method of adjusting the prices of the more and less 
valuable species is believed to accord with customary business 
practice. Volume of money handled, rather than quantity 
of this or that product, is the usual basis for figuring carrying 
charges, depreciation and returns. In logging, improvements 
are frequently constructed primarily to take out certain valua- 
ble species. Inferior timbers may be cut or left as the market 
warrants. In such cases operators will usually cut inferior 
species if a profit can be netted over bare operating costs, figur- 
ing that the cost of improvements is borne wholly by the better 
stufif. The foregoing is believed to be a logical and rational 
application of this principle." 

For a mixed stand, the method proposed is, therefore, to com- 
pute the operating costs on the basis of the total amount to 
be logged, including inferior species. The profit and deprecia- 
tion are then determined as a lump sum, sufficient to pay the 
required per cent on the total investments. Finally, this sum 
is charged as an additional "cost" against the sale value pro- 
rated as outlined above between the different species. The 



STUMPAGE VALUES 191 

remaining margin between the sale value of a species and these 
total charges is its appraised stumpage value. 

181. Carrying Charges versus Profits, on Stumpage. — In 
Chapter X (§ 158), it was demonstrated that a forest capable 
of producing annual income was also capable of paying increased 
taxes, for the reason that compound interest did not accumulate 
on such a forest. The owner may, for his own information, 
and to gauge the advisability of reinvesting income, compute 
the interest on his investment for the interval elapsing between 
cost and the income directly resulting from such cost. But the 
total cash investment in the business does not increase by reason 
of this interest. Neither the unearned interest, nor the actual 
cash expenses for taxes and protection serve to increase the capi- 
tal cost of stumpage, as long as sufficient income is secured each 
year from some portion of the forest or business to cancel these 
costs. 

There is the same difference between tracts of mature stumpage 
held for speculation without cutting, and tracts on which an 
operation is conducted, as there is between an even-aged and an 
all-aged forest, Cases A and C (§ 158). The first case is paral- 
leled by the young forest; the second, by the forest already 
capable of revenue. For timber, or that portion of the timber 
holdings which cannot be cut for from 20 to 40 years, a separate 
cost account based on economic factors (§ 106) would show iden- 
tical costs, whether or not the specific stand is a part of a large 
holding which produces annual revenue, or is part of a specula- 
tive holding producing no income. But there is an enormous 
specific difference in the financial status of the owners of the 
respective tracts, which has an important bearing on the problem 
of carrying charges and increased stumpage values. 

The non-productive speculative holding requires an increase 
in stumpage values sufficient to ultimately offset all annual 
expenses, and earn compound interest on the entire investment, 
up to the year when cutting begins, in order to show a profit 
sufficiently large to include an enterpriser's gain (§ 33). 

The productive holding, which is being operated, and is pro- 
ducing annual income at the present time, will under certain 



192 FOREST V.\LUATION 

conditions continue to pay a profit as great as it pays now, if 
stumpage does not increase in value, or, rather, if the margin of 
prices over. cost of operation does not increase in per cent (§ 187). 
Were the forest itself composed of stands of all ages, which 
are cut upon reaching maturity, this condition would actually 
occur, and advancing prices for stumpage would simply increase 
the profits. 

The conditions confronting the holder of stumpage, who is 
also an operator, partake of both of these extremes or He between 
them. The total investment in stumpage is not maintained, 
except through extending the area by purchase, but diminishes 
constantly by cutting, with a corresponding lightening of the 
annual carrying charges, and a reduction of the capital invest- 
ment (§175). 

It is hardly to be expected that a company planning extensive 
operations over a long period, will inaugurate a scheme of cut- 
ting so comprehensive that they will be enabled to earn their 
carrying charges for the first few years, and at the same time 
pay dividends on the total capital investment. The actual 
annual outlay may absorb every cent of annual income for a 
while. When interest on bonds is added to other carrying 
charges the burden in the earHer years is still heavier, and it 
may require additions to capital to meet these charges. Some 
companies owning extensive timber properties have lost this 
timber by foreclosure, because of non-payment of interest on 
bonds through inability to obtain this additional capital. 

With reduction in interest on bonds, in taxes and in other 
expenses, a company comes sooner or later to a condition per- 
mitting of the payment of dividends. Up to that time, it might 
be assumed that the value of stumpage must increase, in order 
that the dividends when received shall be large enough to com- 
pensate for their absence in earher years. From then on, with 
both the annual expenses and dividends paid from the annual 
net income, an increase in stumpage value or in net income 
means a corresponding increase in surplus and dividend rates. 
When a company is able, by operating, to secure a sufficient 
net income to meet all expenses and pay dividends from the 



STUMPAGE VALUES 1 93 

start, stumpage value does not need to increase beyond the 
amount needed to meet any increased costs, in order to maintain 
the dividend rate. Furthermore, this rate is certain to in- 
crease, on account of reduced carrying charges, even if the value 
of stumpage remains stationary. 

The claim that the value of stumpage must increase at a 
rate sufficient to return compound interest on all costs, or the 
result will be financial loss or bankruptcy, must therefore be 
flatly rejected except for purely speculative holdings, or for 
operators attempting to carry far larger holdings than they 
can take care of with their own capital. An owner of stumpage 
must either have sufficient capital to carry all charges for an 
indefinite period, or he must operate and obtain revenue annu- 
ally. In either case, if he expands his operations by borrow- 
ing on the security of the timber, he must conduct such a 
transaction with considerably greater caution and conserva- 
tism than is necessary in many other forms of business, or 
he may lose his holdings. For a concern which is earning 
annual dividends, increased costs, especially taxation, is the 
only factor which will necessitate the reahzation of higher values 
in order to maintain profits. Very strong combinations of 
capital holding timberlands and operating, may, by a policy 
of cutting calculated to cancel carrying charges, put themselves 
annually in a better financial condition, until, after the period 
of pressure and over-production has passed, they will reap 
relatively large profits, representing more than average divi- 
dends on outstanding capital investments. 

This distinction between the separation of a business into 
parcels, and the treatment of the business as a unit, is recog- 
nized by the U. S. Commissioner of Internal Revenue in inter- 
preting the income tax law as applied to corporations dealing in 
timberlands. A cost account is to be kept for each parcel of 
land as the basis for determining net income (§25), and on sale 
of this parcel the value received can be reduced by the amount 
of the original cost of the parcel, but cannot be absorbed by 
applying it to cancel capital cost for any other parcel. On the 
other hand, net income is treated as applying, not to the parcel. 



194 FOREST VALUATION 

but to the entire business of the concern. If actual cash ex- 
penses in any year exceed actual income, such expenses can be 
added to capital cost, and pro-rated among the parcels. The 
net income, after subtracting capital cost of the parcel sold, 
may be used, as far as needed, to cancel actual outlay on the 
entire tract for the year, the surplus income remaining after 
this total expense is met being the only portion subject to the 
federal income tax. 



CHAPTER XII 

FUTURE VALUE OF FOREST PRODUCTS 

182. Factors Affecting Future Value. — Since the value of 
forest property is derived from income, an appraisal of the future 
value of forest products must precede that of the property 
itself and forms the basis for this appraisal. The examiner 
must base his conclusions, first, on the character and present 
condition of the property and its probable productiveness, and 
second, upon the factors which will affect the value of the prod- 
ucts secured. The elements demanding consideration are: 

The Stand. 

Growth in volume. 
Improvement in quality of products. 
Deterioration of standing timber. 
Closeness of utilization. 

Price Levels. 

General price changes. 

Changes in prices for forest products. 

Effects of substitutes for wood. 

Future Operating Costs. 
Local Factors. 

Future transportation facilities. 

Industries and markets. 

Future supply of timber. 

183. The Stand; Growth in Volume. — The future growth 
in volume of a stand of timber may be predicted for short periods 
by measurements of past growth on average trees. For periods 
exceeding a decade this method becomes unreliable by reason 
of the progressive loss in numbers and altered rate of growth 
of single trees which takes place in all stands as they increase 

195 



196 FOREST VALUATION 

in age. Yield tables attempt to state the actual results in volume 
per acre, produced by stands at different ages. When applied 
to young timber growing upon sites of the same quality, and of 
approximately equal density or degree of stocking, the growth 
and future volume of such stands is predicted with sufficient 
accuracy. For scattered timber or poorly stocked stands, a 
reducing factor is required to prevent over-estimates. Methods 
of studying and predicting yields per acre form part of the 
subject of forest mensuration. Tables of growth and yield 
are published by the U. S. Forest Service and in various state 
bulletins, but are still very deficient in number and reliability. 

184. The Stand; Improvement in Quality of Products. — 
Volume alone does not measure the increase in value of a stand 
of timber. As the trees become larger, the quahty of the prod-^ 
ucts which may be cut increases, for two reasons. The lower 
branches on young trees form knots as long as they remain 
attached, either alive or dead. After the branch falls and the 
scar heals, the wood laid on is free from knots, or clear, and 
produces the most valuable grades. The slabs contain the 
greatest per cent of clear lumber of any portion of the tree, and 
old trees contain enormously greater per cents of high-grade 
products than young timber. The second factor of increase 
in quality is due to the larger sizes which can be cut from older 
trees. Both in length and breadth, higher prices are paid for 
increased dimensions. 

Both volume and quality increase the value per acre entirely 
independent of changes in prices due to economic conditions 
outside the stand. 

185. Deterioration of Standing Timber. — After timber 
reaches a certain age and condition, the stand as a whole ceases 
to increase in volume, and at a much later period it begins to 
diminish in quaUty as well. The trees continue to grow as 
long as they Uve, but the total growth of the stand is offset by 
the loss of trees through windfall, insects and disease. 

The remaining trees are putting on clear lumber, but in old 
stands, decay caused by fungi becomes increasingly prevalent, 
and finally offsets this increase in quahty. 



FUTURE VALUE OF FOREST PRODUCTS 1 97 

In Washington it was shown that Douglas fir stands yielding 
65 thousand board feet per acre at their maximum, deteriorate 
to 25 thousand feet in 100 years, an average annual loss of 400 
board feet in volume alone. Similar losses are occurring in all 
over-mature stands regardless of species or locality. 

186. Closeness of Utilization. — Present volume of standing 
timber is expressed in terms of the quantities actually utilized 
rather than the cubic contents of the stand. A future increase 
in the closeness of utilization thus has the effect of increasing 
the apparent volume of the stand. Its effect on future income 
is of similar importance to that of actual growth in volume and 
quality. In regions where markets for the poorer grades are 
uncertain, these grades are seldom manufactured or included in 
an estimate (§172). The future increase in merchantable volume 
from closer utilization alone is a large factor. 

In addition to the gain in volume per tree the total merchant- 
able yield of the stand is increased by removal of smaller trees 
and of species formerly unprofitable. 

187. Price Levels; General Price Changes. —General changes 
in prices, caused by fluctuations in the value of money (§3) 
would raise the cost of logging and milling in equal ratio to 
the value of the product. When the ratio of profit to costs 
remains the same, stumpage values will increase at the same rate 
or per cent as will prices for lumber. For instance, should 
lumber, now worth $15, increase to $20, or 33^ per cent, stump- 
age value worth at present $3 should then be worth $4. In 
this case costs might be assumed originally as $9.60 and profit 
$2.40, or 25 per cent of cost. An advance of 33I per cent in 
prices of supplies and labor would bring costs up to $12.80, and 
25 per cent profit would equal $3.20, or a total of $16, thus 
leaving the required margin of $4 for stumpage. 

Prof. Irving Fisher predicts an average annual increase in 
general prices of 2 per cent per year for the next fifteen years.* 

188. Price Levels; Changes in Prices of Forest Products. — 
The prices for a given product will depart from the average 

* American Economic Review, Sept., 1912, Vol. II, No. 3, p. 553. Managing Edi- 
tor, Prof. Davis R. Dewey, 491 Boylston St., Boston. 



198 FOREST VALUATION 

price level when the demand for the specific goods increases 
relatively faster than the supply. Both demand and supply may 
be increasing, or both decreasing, or demand may increase while 
supply diminishes. In any case, the effect on prices is gauged 
by the difference rather than by the direction of these forces. 

When population is increasing, while the area occupied by 
timber tends to decrease, the maintenance of the same per capita 
rate of consumption for timber causes demand to progressively 
outrun supply; and this factor has resulted in the past two 
decades in an increase in lumber prices approximately twice 
as rapid as the movement of prices in general. This increase 
has had a pronounced effect on stumpage values. Instead of 
increasing by the same per cent as the price of lumber, the value 
of stumpage tends to absorb the entire surplus not taken by 
increased costs (§ 170). The profits of the logger and millman 
tend to maintain a fairly constant ratio to cost of operation, 
except where, by retarding the advance in stumpage values, 
they are able to appropriate a larger share of this increase. 
In the above illustration, the price of lumber can be assumed to 
have increased from $15 to $25, or 66f per cent, while general 
prices and the cost of logging advance but 33§ per cent. If a 
profit of 25 per cent on operating costs is still considered satis- 
factory, these costs advance only to $16, and the margin of value 
for stumpage becomes $9, an increase of 200 per cent. 

In regions where timber was formerly barely accessible (§ 1 74) 
this increase in value sometimes amounts to several hundred 
per cent on cost. Stumpage in general doubled and trebled 
in value in most regions of large supphes in the decade of 1898- 
1908. 

189. Effects of Substitutes on Wood Prices. — Increasing 
prices for lumber and other wood products act in two ways 
to diminish consumption of wood. Less wood is used merely 
because it costs more and the enterprises depending on wood 
are curtailed; and substitutes appear, made possible by this 
same increase in price. 

The extent to which substitutes will succeed in permanently 
displacing wood as a raw material depends upon three factors: 



FUTURE VALUE OF FOREST PRODUCTS 



199 



The relative adaptability of wood and its substitutes for 

the services demanded. 
The relative cost, measured in first cost of raw material, 
labor of construction and durability or cost of deprecia- 
tion. 
The habits and customs of consumers as influenced by 
advertising and imitation. 

When no substitutes can be found which will give the kind 
of service demanded, the use of wood will be continued, at 
constantly advancing prices, until the supply is completely 
exhausted, when the need for which this wood was used will 
remain unsatisfied. But ordinarily, high prices will force the 
use of some substitute which, while not so satisfactory, is so 
much cheaper that it is accepted. 

Formerly wood was used for many purposes because it was 
cheaper than substitutes. Board fences and sidewalks have 
been replaced by wire and cement, since the combined cost of 
labor, material and depreciation is less for the latter materials 
and they give better satisfaction. 

Wood for buildings has until recently been much cheaper 
than brick or stone, there being a saving in labor and material. 
Old, well-constructed wooden houses depreciated slowly. At 
present it is still cheaper to build wooden houses, but there 
is less difference in the cost of materials, while the poor quality 
of much of the lumber used increases depreciation in favor of 
brick, cement or stone. A further element of cost is the insur- 
ance of wooden buildings demanded by the extra fire risk. 

The use of wood for boxes and crates has been considerably 
lessened by substitutes in the form of fibre and cardboard, 
which are cheaper and fully as satisfactory for many purposes. 
Shingles have been extensively replaced by patent roofing which 
is cheaper in both labor and material, although possibly not 
as durable. 

The effect of advertising and habit is especially noticeable in 
the last two instances. Manufacturers of patent roofing and 
of cheap boxes have expended large sums to capture the trade 
and educate consumers into using their products. Such changes 



200 FOREST VALUATION 

are made with reluctance and suspicion, but once undertaken, 
the imitative faculty, which plays so strong a part in human 
affairs, may cause a very rapid extension of the substitution 
and force producers of lumber to fight for the retention of trade 
formerly theirs by right of original possession. 

In spite of the inroads which substitutes have made on 
consumption of wood as the result of high prices and trade de- 
velopments, there remain many uses for which wood is so pre- 
eminently adapted, that the total consumption is almost certain 
to increase in the future rather than to diminish. For railroad 
ties, the resilience or elasticity of wood, which absorbs the shock 
of traffic, combined with the small labor cost of track repairing, 
and increased safety of travel, when compared with the sub- 
stitutes so far employed, make it certain that the price of rail- 
road ties will be much higher than at present before the railroads 
discontinue the use of the wooden tie. 

A still more striking case is the use of wood for paper pulp. 
Formerly confined largely to spruce and poplar, pulp is now 
made from many hardwoods and from southern longleaf pine. 
Paper can be made from many other materials, such as rags 
or corn stalks, but the cost of assembling sufficient quantities 
at the mill is greatly in favor of wood. 

The general effect of substitutes is to diminish the use of 
cheap grades of wood, and to increase the supply available for 
more important uses. This tendency is illustrated in the case 
of fuel. Wood for domestic fuel is still used in enormous quan- 
tities, but only at points near the source of supply. Its bulk 
and weight prevent its transportation by freight for long dis- 
tances to large centers of consumption. It is probably worth 
as much, if not more, for this purpose in most localities than 
it ever was. It would have been impossible for our forests to 
supply enough fuel for the entire demands of modern industry. 
The substitution of coal has relegated wood to the position of 
a luxury for the fireplace in most large cities; has ruined the 
markets for cordwood formerly existing in connection with cer- 
tain manufacturing enterprises, and in some regions near such 
factories has caused the value of woodlands to decline. Yet the 



FUTURE VALUE OF FOREST PRODUCTS 201 

general effect of this substitution, where the market has been 
spoiled for cordwood, is to encourage the growth of timber of 
larger dimensions, suitable for ties, telegraph poles and lumber, 
from which the owner may realize eventually as large a profit 
as from his cordwood. Substitutes thus tend to bring about 
longer rotations, greater diversity of wood products, higher 
values per acre, and increased usefulness of each acre of forest, 
and do not, in general, interfere seriously or permanently with 
the industry of wood production. Radical changes in the man- 
agement of forests may become necessary by these economic 
changes in utilization and markets, and the rate of interest 
earned in private forestry may be diminished by the necessity 
of longer rotations and more specialized products. New uses 
for wood spring up to take the place of former demands now 
obsolete. 

The use of substitutes will undoubtedly prevent wood prices 
from rising as rapidly as in the decade 1 898-1 908 and probably 
explains in some measure the slower increase which has occurred 
since that date. But substitutes will never do away with the 
use and demand for wood, nor cause the average value of wood 
products and timber stumpage to be lowered to any appreciable 
extent. Prices are still far below the level established in Europe, 
and it is reasonable to expect that these prices will continue 
to increase slightly faster than those for other goods, for some 
time to come. 

190. Future Operating Costs. — Future costs of logging and 
milling will increase approximately at the same rate as general 
prices. Added to this are the special factors which may cause 
operating costs to vary from this general trend. 

The cost of labor is the largest item in logging. Throughout 
northern regions the effectiveness of woods labor is rapidly di- 
minishing. Old-time American lumberjacks are very rare, and a 
large part of the work is performed by inexperienced foreigners, 
or shifting labor from the city slums, resulting in an increased 
cost considerably greater than can be accounted for by increased 
wages. This tendency is offset by improved efficiency, as 
operators learn from experience the use of the best technique. 



202 FOREST VALUATION 

The recent development of logging engineering as a profession 
on the Pacific Coast is in response to a recognition by operators 
of the possibility of greater eflficiency and economy in trans- 
portation. 

Extraordinary increases in cost, if general-, must ultimately 
be taken from the value of stumpage. In the same way, a gen- 
eral reduction of costs, even if due solely to improved methods 
and greater efficiency, will increase the value of stumpage. 

191. Local Factors: Future Transportation Facilities. — 
With increasing population, transportation facilities are certain 
to improve. Tracts of timber of considerable extent and volume 
will be certainly reached in time by the construction of railroads 
or other special means of transportation. A far more serious 
question arises as to the permanence of such facilities. If there 
is not sufficient use for them to justify their continuous main- 
tenance after the present merchantable stand is removed, they 
will be abandoned. The rails and ties are removed, the flumes, 
bridges, trestles and corduroy rot away, the grades become gul- 
lied and the roads grow up to brush. To remove any timber 
in the future these structures must be replaced. There must 
be a sufficient stand of second growth not only to furnish the 
material for reconstruction but to warrant the expense (§98). 
The original stand of virgin timber may have been several hun- 
dred years old, and far more valuable per thousand feet than 
this second growth (§ 184). There are many districts where a 
second operation will be financially impossible, and timber 
grown after logging will remain inaccessible unless a very con- 
siderable increase occurs in the value of stumpage in general. 
This condition applies to mountainous or non-agricultural re- 
gions. Elsewhere, increasing population assures a future market 
for all timber. 

A similar increase in average transportation costs per thousand 
board feet occurs with the exhaustion of the more accessible 
bodies of virgin timber. This tendency was for a long period 
overcome by a corresponding expansion of the size of operations, 
the amount of capital invested, and the quantity of timber 
tributary to a single transportation system. The old days of 



FUTURE VALUE OF FOREST PRODUCTS 203 

hand logging, short drives and heavy timber were succeeded 
by large operations, which tapped reservoirs of timber of great 
extent, and distributed the costs over enough stumpage to bring 
them even below those of the simpler undertakings. When 
this increasing cost is no longer ofifset by increased volume to be 
transported, it at once depresses stumpage values. This means 
that average quoted prices for stumpage may not rise as rapidly 
as lumber prices, because the later quotations are for stumpage 
differently situated. The rise in values occurs, but is evident 
only for the same or similar timber. 

An important consideration in forest production is the pos- 
sibility of substituting the cost of growing trees in accessible 
situations, for the cost of transportation from regions much 
farther from markets. As accessible timber disappears, the 
difference in stumpage value between timber easy and difficult 
to obtain will become larger and larger, and this margin of value 
can be expended upon forest production on accessible sites. 

192. Local Factors : Industries and Markets. — Transpor- 
tation charges are subtracted from income in arriving at stump- 
age value. It follows that the farther from the mill the timber 
lies, the less will be its value. In the manufacture of lumber, 
portable mills brought to the timber greatly reduce the cost 
of hauling this lumber to the market by leaving the waste from 
sawing in the woods. But the greatest value for many woods 
lies in their use for special products, such as spools, excelsior, 
boxes, match stock and other specialties. These factories 
pay larger prices for stumpage since they utiHze the tree far 
more completely and obtain much greater returns on a given 
amount of wood. Local industries of this character must 
operate continuously in order to be profitable. They remain 
in a region as long as they can obtain a sufficient supply of raw 
material. The reduction of the supply to a point where the 
mills can only run part time, or must suspend operations for 
several years, results in driving out these industries. The 
remaining stumpage must then be marketed at more distant 
points, perhaps for a less intensive use, and there is a very con- 
siderable loss in value. 



204 FOREST VALUATION 

193. Local Factors : Future Supply of Timber. — From the 
factors discussed in Articles 191 and 192 it is apparent that the 
local value of timber stumpage in the future depends largely 
upon the total quantity of timber produced in that locality, 
and the continuity of the supply. If virgin timber is being 
appraised, its value must often be based on the premise that it 
will be logged at the time the remaining stumpage is cut, since 
it is worth more now than it may ever be again. If the timber 
is of second growth, or is in a region of second growth, the extent, 
average age, vigor and utility of this second growth is of the 
greatest importance in appraising the value of any separate par- 
cel or tract. Where most of the cut-over areas are ravaged by 
fire, or otherwise rendered worthless, an isolated patch of repro- 
duction or plantation not only costs more to protect, but its 
stumpage value is permanently less in such a region than if it 
were a part of an abundant second growth. It may pay better 
to plant trees in regions where natural reforestation is abundant 
than under the reverse conditions. By following out this argu- 
ment it will be seen that extensive operations on the part of 
states or the national government to protect and reproduce 
large areas of forest will have the effect of raising stumpage 
prices for those private owners who grow trees in such 
localities. 

194. The Rate of Increase in Stumpage Value. — By care- 
fully weighing both general tendencies and the equally important 
local factors, the examiner may appraise the probable stumpage 
value of timber with considerable accuracy for a period of 10 to 
15 years in the future. Beyond this period, so many unforeseen 
events may occur to affect prices that only a semblance of accu- 
racy can attach to such appraisals. One of two suppositions 
can be made. The value may be assumed to remain constant 
beyond a certain year. The tendencies of prices and the 
history of wood consumption justify so conservative a con- 
clusion. 

The second assumption is that prices will continue to advance 
at the same per cent as in the past. The validity of this con- 
clusion depends upon the meaning attached to the phrase; 



FUTURE VALUE OF FOREST PRODUCTS 



205 



whether simple or compound interest is meant, that is, whether 
the original value or the increasing value is the basis of the 
annual percentage. Stumpage as a residual value is subject to 
more extensive proportional changes than the price of timber 
products which causes these changes (§ 188). Then, while prices 
and stumpage value may rise at a rate equal to simple interest 
on the value at a given date, the rate of interest, simple or com- 
pound which this rise represents, when based on increased prices 
or values, becomes less and less. 

Table V illustrates these relations. Should stumpage rise 
from an original value of $5 per thousand, by the sum of $5 
every 10 years, or 50 cents per year, the rate of increase would 
be equivalent to 10 per cent simple interest annually on the 
original value. 

TABLE V 

Rate of Annual Increase in Value of Stumpage 



Period, 

years. 


Value of 

stumpage, 

dollars. 


Rate of simple 

interest on 

original value, 

per cent. 


Rate of com- 
pound interest 
on original 
value, 
per cent. 


Rate of simple 
interest on 

value for each 
decade, 
per cent. 


Rate of com- 
pound interest ] 
on value for 
each decade, 
per cent. 





5.00 
10.00 
15.00 
20.00 
25.00 
30.00 










10 

20 
30 
40 
SO 


10 
10 
10 
10 
10 


7.2 
5.6 
4-7 
41 
3-65 


10 
5 
3-3 

2-5 

2 


7.2 

41 
2.9 

2-3 

1.85 



Values of stumpage are more apt to follow the law of increase 
set forth in this table than to increase continuously at a fixed 
rate of compound interest. It follows that as prices and values 
advance, the rate of increase must fall. By first predicting the 
amount of the increase, or the rate expressed in terms of simple 
interest on original value, the rate of compound interest for 
these values may be computed if desired (§ 89, Formula XIV; 
see also § 49) . 

The true rate of increase in stumpage value depends upon 
the sum of increased values due to growth in volume, improved 
quality, closer utilization and price increment. These sources 



2o6 FOREST VALUATION 

may be expressed separately, as if each represented a rate of 
interest, as 

Vo(i.oa){i.ob)ii.oc) = Vi, 

which is slightly greater than 

Vo -i.oia + b + c) = Fi. 

In ascertaining the values of the factors a, b, etc., for a period of 
some years, these values must either be taken as representing 
simple interest, or, if compounded, the rate quoted for the 
entire period must be much lower than the probable annual 
increase in the earlier years. 

195. Increasing Future Values as a Basis of Appraisals. — 
As set forth in Article 139, the elements of increase in value 
inherent in the character and condition of the property itself 
must be accepted as reliable and occurring in the natural course 
of events, and will be recognized in appraisals for public purposes, 
such as damage suits and condemnation proceedings. These 
include growth and quality increment. But the factors of 
closer utilization and rising prices depend upon outside influ- 
ences shown to be affected by a complex of causes and therefore 
not capable of reliable diagnosis. 

The acceptance of such increased prices as a basis of appraisals 
must be determined by the purpose of the appraisal, and by 
the evidence on which the conclusions rest. Reasonable con- 
servatism is required in appraisal of damages. A more liberal 
construction is permitted in condemnation proceedings. In 
either case, evidences to prove the probability of rising prices 
must take into account both the general and local factors dis- 
cussed in this chapter, and it will usually be found advisable 
to make very moderate claims on this score. 

As a basis of valuation to determine a tentative sale value, 
it is equally necessary to treat the element of future prices 
conservatively. The purchaser is entitled to this source of 
future profits, and should base his price for the property upon 
present rather than future prices for products. As tending 
merely to show the probable amount and present value of these 



FUTURE VALUE OF FOREST PRODUCTS 207 

profits, for the information of the owner, no objection can be 
urged to any assumption which he can reasonably justify. 

196. Revision of Stumpage Values in Long-term Contracts. — 
In timber sale contracts, where timber is paid for at time of 
purchase, the owner of the stumpage, in return for the risks 
incidental to carrying this investment, is entitled to share in 
the increased values which may materialize (§176). For periods 
of less than five years this factor is immaterial. If the contract 
is for longer periods, at a fixed price, the purchaser is usually 
willing to operate at a loss durmg the earlier portion of the term, 
in expectation of realizing increasing profits later on. In this 
way the increase may be shared with the owner even on the basis 
of a fixed contract price. Contractors desire certainty in the 
element of cost of raw materials, even at some sacrifice of possible 
profits. 

The ideal arrangement is some form of revision at stated 
intervals, by which the value of stumpage is readjusted to 
changing conditions. Such a revision may be based on a reap- 
praisal. This would take into account the element of closer 
utilization, as well as advancing prices. The factor of growth 
is accounted for by the scale, while changes in quality are usually 
neglected, but can be considered in reappraisal. This method 
is advocated in the Forest Service for regions where close compe- 
tition exists for government timber. 

A second plan for revision confines the changes to the single 
factor of prices for lumber, neglecting those of utilization and 
quality. The point to be determined is the per cent of increase 
in lumber prices which should be appropriated by stumpage. 
On the basis that timber prices have advanced in the past 
more rapidly than costs, the Forest Service has claimed as much 
as 75 per cent of this increase for stumpage. Their present 
basis is to appropriate 50 per cent of increased prices as stumpage 
value. Revision, without reappraisal, is undertaken at intervals 
of five years. The prices of lumber accepted as a basis (§172) 
are averaged for three years previous to revision. 



CHAPTER XIII 

RISKS 

197. Risks versus the Rate of Interest in Forestry. — The 

risks to which forest property is exposed tend to discourage 
the investment of funds in forest production, in the same manner 
that similar risks restrain investors in other enterprises. This 
tendency is expressed by an increase in the basic rate of interest 
at which capital will seek investment in forestry {p per cent). 
A high rate of interest is the expression of a fear entertained for 
the safety of the principal. The use of such a rate gives very 
low expectation values for probable future income. 

When the per cent which can be earned by forest enterprises 
is lower than the rate of interest demanded, capital is presum- 
ably unwilling to invest in forestry because the average risk 
of loss exceeds the probable income. Should individuals still 
be willing to undertake forestry, they do so because they place 
a lower estimate upon this risk than that commonly prevailing, 
or expect to combat it by effectual preventive measures; hence 
their individual "rate of interest" is gauged proportionally 
lower and indicates possible profit. 

198. The Character of Risks in Forestry. — Risks may be 
classed as physical, moral and financial. Physical risks are 
those incurred through the operation of the forces of nature. 
In case of fire, the physical risk is greatly increased by the addi- 
tion of a moral risk. Moral risks are those arising through 
possible human actions, either deliberate or accidental. Finan- 
cial risks include both physical and moral elements, since all 
risks are measured by the probable financial losses that may be 
inflicted. But the risk of loss of profits exists quite independent 
of these other factors, and is influenced by changing economic 
conditions, such as demand, prices, future taxation and any other 

208 



RISKS 209 

element which serves to diminish profits below the expected 
amount. 

199. The Gauging of Risks. — There are two elements to a 
risk: the hazard, or degree of probabiHty that damage will 
occur, as indicated by past history and present conditions; and 
the liability, or value of the property subject to damage. The 
liability, in forest investments, is measured by expectation 
value for partially mature stands; but for plantations, cost is 
the basis considered, and extra efforts will be made to protect 
such plantations because of the investment which they represent. 
The hazard must be gauged, during the growth of the crop, by 
the increasing or decreasing susceptibility or resistance of the 
trees to fire, wind, insects and fungi, and by the probability of 
these events occurring, through prevalence of the causes. 

When the liability is large, and the hazard is extreme, active 
preventive measures involving considerable expense are jus- 
tified. 

With a small present liability and extreme hazard, the ques- 
tion arises whether protective expenses will pay for themselves. 

WHien hability is large, but the hazard negligible, protective 
measures may involve a needless expense, and diminish profits 
and value. 

With small present liability, and negligible hazard, the ex- 
penditure justified for forest protection is still further reduced. 

The financial character of the risk thus indicates the expense 
which should be incurred for protection. The largest expen- 
ditures are justified when property of considerable value is in 
great danger of being destroyed. 

200. Physical Risks : Fire. — Fire is by far the greatest 
risk in forest production. The resistance of trees to fire damage 
depends on the character of the bark, which differs with the 
species, and on its thickness, which increases with age for all 
species. Sandy soils in all regions are far more subject to fire 
than soils which retain moisture. In many locaHties fires burn 
annually on such sites. As a consequence, the tree species 
which inhabit these situations have developed a fire-resistant 
bark which often renders them immune to the effects of ordinary 



2IO FOREST VALUATION 

fires. This immunity is attained at an early age, but seldom 
covers the period of reproduction, or the seedling stage of growth. 

On soils and in localities where fires burn only at long intervals, 
most tree species are very susceptible to injury, and, as the 
fires which do occur on these sites are unusually severe, practi- 
cally the entire stand may be killed. The younger the stand, the 
greater the per cent of mortality and consequent proportion of 
value destroyed. 

The fire hazard is largely due to the inflammable character 
of the forest floor. The entire mass of accumulated litter and 
humus will burn when dry enough. Most of the undergrowth 
is also extremely inflammable. Shade thrown by a dense cover 
reduces the risk by preventing extreme desiccation, and keeping 
out brush and grass. Of the materials forming the forest floor 
and undergrowth, grass, when dry, is the most inflammable. 
Pine needles come next, while hardwood leaves do not cause a 
serious blaze. Humus or duff, when dry enough to burn, causes 
a slow and very destructive ground fire, difficult to extinguish. 

The hazard is reduced by atmospheric moisture. Except on 
the sandiest soils, belts of heavy rainfall will give rise to rank 
vegetation. These are^ regions of slight hazard. Over most of 
the forest areas in this country droughts occur either annually 
or at greater intervals, of sufficient severity to create an exces- 
sive fire hazard. 

This risk is enormously increased by logging, because of the 
great increase in litter and slash incidental to the operations. 
As the liability is reduced in like proportion, the temptation 
to ignore the hazard and abandon the attempt to protect the 
residual forest values is very great. 

201. Wind. — Wind resistance is greatest with small timber, 
and becomes less with increasing bulk, weight and age. The 
form, distribution and penetration of the roots of different 
species determine their resistance to wind-throw. Shallow, 
rocky soils, or those underlaid by hardpan or water, induce 
windfall. Regions subject to frequent tornadoes present a 
wind hazard which must be reckoned with in planning the 
sequence of logging operations. This risk is excessive only for 



RISKS 211 

mature and over-mature timber, and is a serious factor in opera- 
tions where a portion of the stand is left for a second crop or as 
seed trees. If all parts of a tract are accessible, wind-thrown 
tim_ber can be marketed without loss, provided the quantity- 
thrown does not exceed the capacity of the operation as gauged 
by the length of time the down trees can be left without deterior- 
ation. 

202. Insects. — Imported insects as, for example, the gypsy 
and brown-tail moths are far more dangerous to forests than 
native insects, as they are practically without any natural 
parasites. The introduction of these enemies now promises to 
keep the gypsy moth in check. 

Native insects occasionally develop possibilities of injury, 
and may destroy great areas of forest. They are finally checked 
by disease or parasites. The worst of these insects are the bark- 
boring beetles. Defoliating insects, like the larch sawfly or 
spruce bud worm, may kill timber over entire regions. The 
destruction of native birds explains the increase of certain 
forms of injurious insects. Woodpeckers are very useful in 
keeping boring larvae under control. 

203. Fungous Diseases. — The only conspicuous instance of 
widespread destruction of an American species due to fungous 
attacks is found in the ravages of the imported disease of the 
chestnut, Diaporthe parasitica, which threatens to exterminate 
what is considered the most important commercial hardwood 
over wide regions east of the Appalachians. Great damage is 
done to the heartwood of all species of trees by fungi which 
gain entrance through wounds or knots. These fungi do not 
kill the trees as they have no effect on the living tissue. This 
damage is greatest in old timber and is not a serious factor in 
second growth. 

204. Climatic Injuries. — Excessive drought in rare instances 
kills many trees of the more susceptible species in exposed 
regions or localities. Trees unused to swampy conditions are 
killed by prolonged flooding of the roots. 

Minor injuries are caused by breakage in sleet storms or heavy 
snows, permitting fungi to enter. Reproduction is especially 



212 FOREST VALUATION 

sensitive to frost, drought and excessive moisture, but the 
young trees soon become hardy. 

205. Injurious Fumes. — - The physical injury caused by 
fumes is due to human activities. The fumes from copper 
smelters will sometimes kill timber seventy-five miles from the 
location of the smelter.* 

206. Moral Risks : Trespass. — Timber products are fre- 
quently stolen, but the theft is easily discovered, and it is not 
difficult to identify the trespasser. Losses from this source are 
the result of neglect of the property, and are easily eliminated by 
proper marking and posting of boundaries, and the employment 
of a custodian. The expense of such protection is serious for 
small tracts whose owners reside at considerable distances, but is 
immaterial for larger holdings. The character of the population 
and ease with which small quantities of timber can be transported 
determine the degree of hazard. 

Trespass is frequent in connection with logging operations, 
where only a portion of the stand is to be cut, or where the logger 
attempts to enlarge his operation at the expense of adjoining 
owners. Reputable firms incur considerable expense in relo- 
cating boundaries not only to prevent others from trespassing, 
but to avoid accidental encroachment on adjoining lands by 
their own employees. 

207. Moral Risks: Fire. — Some fires are started by light- 
ning, but the great majority are due to human agencies. Most 
of these fires are caused by careless or unintentional acts, but 
in some regions the habit of burning is firmly fixed, and occa- 
sionally fires are set through malice. The moral risk thus in- 
curred is so great in some southern states that it presents 
an almost insuperable obstacle to forest production. In other 
localities this risk is chiefly due to avoidable factors, such 
as railroad operation, and yields to preventive measures and 
education. 

208. Financial Risks. — The risk of excessive future taxa- 
tion is discussed in Chapter X. Unless this risk is removed, it 
will prevent the practice of private forestry in the regions affected. 

* Deerlodge National Forest, Anaconda, Montana, 1912. 



RISKS 213 

The financial risk is in reality a summary of the factors 
enumerated above plus the economic risk of failure to 
secure remunerative prices (Chapter XII). The economic 
situation, except in certain inaccessible localities, is so 
favorable that the only serious risks are those discussed in 
this chapter. 

209. Control of Risks : Insurance. — Insurance against losses 
follows rather than precedes other measures for the control of 
risks. When the risk is large, and the probable amount of 
damage uncertain, the premiums will be prohibitively high. 
At the present time, no insurance against fire is in force on 
standing timber in the United States, and no companies will 
accept such risks, Lloyds of London have insured a large 
tract of timber in Canada.* 

The unrehabihty of appraised values in case of damage, and 
the great variation in value of stumpage, adds to the difficulty 
of such insurance projects. Standing timber in European states 
is widely insured at low rates. Tornado insurance on timber 
is available in the United States, but has not been taken ad- 
vantage of by owners of timber stumpage. 

210. Public Measures. — Within the last decade it has been 
demonstrated that the fire risk can be largely eliminated in 
northern and western states by the enforcement of efficient 
fire laws and the organization of state and local forces of fire 
wardens. These systems are as yet not completely successful, 
but promise to become so, especially in states where politics 
has been eliminated from the organization. Education of the 
public, punishment of offenders, and prompt detection and sup- 
pression of incipient fires form the groundwork of these systems. 
Through their operation, risks will eventually be reduced to 
the point where it will become possible to insure standing 
timber from fire. 

These state forces are aided materially by semi-public co-oper- 
ative associations of land owners, which expend large sums in 
fire patrol and suppression. The operations of these associa- 

* " Logging," by Ralph Clement Bryant, p. 37. John Wiley & Sons, Inc., New 
York, 1913. 



214 FOREST VALUATION 

tions are conspicuous in the Pacific Northwest, and have ex- 
tended to Michigan and New England. 

The importation of injurious fungi and insects is now guarded 
against by national statutes and inspection. One serious fungous 
disease, the white pine blister rust, has been checked by this 
means. State inspection and control of injurious insects and 
diseases, supplemented by the activities of the national govern- 
ment, furnish a means of preventing future outbreaks similar to 
that of the chestnut bark disease. Such aid should be chiefly 
preventive in character, and can be invoked but seldom for the 
control of native insects. 

211. Private Measures. — Private owners may be forced by 
state legislation to take measures to eliminate unusual fire risks 
caused by their own operations. Laws making brush or slash 
burning compulsory, especially along rights of way, are already 
adopted in some states. Top-lopping is intended for the same 
purpose. 

In addition to these compulsory private measures, owners of 
forest property must expect to take extra precautions against 
fire, similar to those adopted by factories and stores to supple- 
ment the work of the fire department. Firebreaks should be 
constructed and maintained for the protection of plantations, 
and to guard against excessive hazards. The owner and his 
tenants and employees should be prepared for fire fighting and 
equipped with the most suitable tools for the purpose. 

212. Effect of Risks on the Business of Forest Production. — 
Mature timber, while in danger of being killed by fire, insects 
or disease, or blown down, can usually be salvaged with only 
partial loss. To the greatest danger of all, fire, it is moderately 
resistant. Since systematic fire protection has been instituted in 
the North and West, losses have averaged less than two-tenths 
of one per cent annually, on the value protected. The risk has 
never deterred investors from making purchases and speculating 
on values of stumpage. 

With young, immature timber and reproduction, the same 
cannot be said. A comparison of risks shows that the hazard is 
less on small or young trees, from practically all sources excepting 



RISKS 215 

fire. But the risk of destruction from this source has in the 
past been so great as to constitute a prohibitive hazard. De- 
struction of young timber is a total loss, for there is no salvage. 
The dead trees are quite worthless, and even constitute an 
additional expense (§136). The period over which the invest- 
ment is exposed to risk is correspondingly longer for young 
timber than for mature trees, which can be removed at the 
owner's convenience. 

As long as the public and the land owners themselves remained 
completely indifferent to young growth, and regarded fires on cut- 
over lands as of no consequence, the risk incurred in the business 
of forest production was prohibitive. One could as well expect to 
succeed in a mercantile business when thieves, incendiaries and 
dishonest debtors abounded, and there existed no effective law 
or public sentiment to check their operations. The first step in 
estabhshing the social conditions which are now making forest 
production possible was the creation of a new public conscience 
and understanding on the subject of forest property and forest 
fires. The ehmination of theft of national and state timber, the 
tremendous progress in fire protection in northern states, and 
the large sums spent in eastern states for suppression of forest 
insects and diseases indicate that this constructive work is 
succeeding. Under proper social conditions, such as have been 
secured in France and Germany, the element of risk in forest 
production becomes less than that incurred in almost any other 
form of enterprise. The employment of a high rate of interest 
in forestry is merely the expression of this undeveloped state 
of civihzation as touching forest property, and should not be 
confused with the returns or earning power of forest invest- 
ments. 



CHAPTER XIV 

FIELD APPRAISALS OF TIMBER STUMPAGE 

213. The Scope of Field Appraisals. — The value of timber 
stumpage, while based on the species, quantity and quality of 
the timber, is determined only when the value of the products 
f.o.b. at mill and the intervening costs of logging and milling 
have been appraised (Chapter XI). 

The field appraisal thus deals first, with the reconnaissance 
of the timber (§ no), and second, with the appraisal of logging 
costs. The cost of milhng, depending as it does on the size of 
the mill and duration of the operation (§ 173), is affected by the 
total volume of timber accessible to the mill, and its ownership, 
and this cannot always be determined when examining a given 
tract. Appraisals, except when they cover a large area, are 
therefore most definite when made in connection with mills 
already operating. 

The choice of general means of transportation must occasion- 
ally be left to the field examiner, but more often this is already 
indicated by local custom, and it remains only to determine on 
the ground whether any modifications of the plan are necessary 
because of the nature of the topography and the transportation 
problems which arise. The scope of the actual field appraisal 
of costs is usually confined to ascertaining the local costs of 
logging. These costs should be appraised separately for each 
so-called "logging chance," or separate body of timber forming 
a logging unit. In flat regions, the division of a larger area 
into units is not important and depends on the convenience of 
locations and routes for main spurs. But in a rough or moun- 
tainous country the ''chance" is a distinct topographic unit, 
such as a gulch or small basin, containing enough timber to 
furnish employment for a camp of reasonable size for one or 

216 



FIELD APPRAISALS OF TIMBER STUMPAGE 217 

more seasons. The timber on such a unit normally comes out 
over the same route — a branch railroad spur or road. 

Of first importance in the examination is the necessity of 
sizing up this local transportation problem, deciding upon the 
best method of removing the timber, and estimating the diffi- 
culties of construction and cost of overcoming them. The cost 
is gauged, not on the basis of the total expense of construc- 
tion, but with relation to the amount of timber reached (§ 174). 
In high and precipitous mountains it is necessary to decide 
how far up the slope the operator can go without exceeding 
the permissible cost of getting out his logs. 

This transportation cost is thus directly dependent upon 
the estimate of the standing timber. The field examination 
necessary to determine it is either a part of the work of timber 
reconnaissance, or some additional work is done following the 
completion of the cruise, to make sure of the salient points. 

214. Timber Reconnaissance : The Map. — In the timber 
examination the tract is ordinarily crossed and recrossed at 
intervals of 40 rods or less, and the intimate and systematic 
knowledge of the topography and surface thus gained permits 
the formulation of the plan for logging. The main drainage 
and its tributaries are located and the character of the slopes 
arid surface noted. 

This knowledge, when necessary, may be systematized in 
the form of a topographic map which shows all features that 
affect logging. If the topography is so level that transportation 
presents no difficulties, such a map serves no useful purpose. 
If the map does not indicate conditions with sufficient accuracy 
and detail to enable the manager to plan the general location 
of his transportation system, it fails of its purpose. Actual 
lines of railroad or road must be located on the ground, but the 
entire system can nearly always be roughly planned from a 
good map. Since such a map can be made as a part of the work 
of timber estimating, the expense is minimized and the effort 
justified. Otherwise the information so vitally necessary to 
the planning of transportation routes exists only in the mind 
of the field examiner or in the form of incomplete notes. 



2l8 FOREST VALUATION 

215. Estimation of Standing Timber. — The estimation of 
standing timber presents one of the most difficult problems in 
the business of lumbering. This might not be true were there 
no limits to the cost which can be incurred in making such an 
estimate. But it is quite possible for a careful detailed measure- 
ment of the timber on a tract to cost over $i.oo per acre. It is 
a recognized precept in business that the cost of stock taking 
must be kept as low as possible, for the work adds nothing to 
the value or the profits of the business, and is necessary merely 
as a basis upon which to plan actual operations. 

Methods of timber estimating are determined by the relation 
between the cost of doing the work and the value of the timber. 
The amount of care and expense justified increases with rising 
stumpage values. Timber is always estimated in terms of the 
product which has the highest market value, or is most readily 
saleable. When pulp wood is used, the cord is the customary 
unit. But should the stand be situated in a region where cord- 
wood is used only for fuel, the number of ties or poles and the 
contents in lumber of suitable trees would be first estimated 
and only the residue expressed in cords. By far the greater 
quantity of timber is estimated in terms of board feet, since 
it is used in this form. 

216. Log Rules. — The measurement of standing trees for 
board foot contents is beset by the fundamental difficulty that 
no commonly accepted standard of measurement has been or is 
likely to be adopted in this country which will properly express 
this contents. Innumerable log rules are in use, of which a 
few are now widely recognized. But these rules are very de- 
fective, seldom giving a sufficiently large contents for logs (§179). 
In spite of this fact, it will seldom be possible to adopt the actual 
sawed output as a basis for timber estimating, as long as logging 
contracts and other woods operations, such as felling, are based 
on the old standards as expressed by the log rules in common 
local use. Any great increase in the measured volumes of the 
logs would require reduction in the scale of payment or result 
in loss of profits by the millman. The only safeguard is a 
knowledge of the amount of overrun usually obtained with the 



FIELD APPRAISALS OF TIMBER STUMPAGE 219 

given rule in the class of timber estimated (§ 179). Quantities 
estimated will therefore be expressed as log contents measured 
by the local rule, but in computing values the overrun on each 
thousand feet of logs will be allowed for. Log rules have been 
devised which give very closely the actual sawed contents of 
logs. The use of such a rule insures a proper standard of meas- 
urement for the contents of standing trees.* 

217. Closeness of Utilization as Affecting Timber Estimates. 
— Another factor which influences timber estimating is the 
closeness with which the timber is utilized (§ 186) . Cheap lumber 
necessitates the wasting of the poorer grades of boards, as the 
cost of manufacture exceeds the sale value. Under this condi- 
tion, limby tops, defective logs and small trees are left in the 
woods. In such forests as exist in Washington State, the differ- 
ence between utilizing only the highest grade product and taking 
common and low grade lumber may make 50 per cent difference 
in the total quantity removed (§ 186). In general, an estimate is 
made on the basis of present market conditions, and does not 
attempt to anticipate future values, though this will have weight 
with a far-sighted purchaser. Estimates made in past periods 
were low compared with present estimates and must be revised 
as utilization becomes more complete. 

218. Field Methods of Timber Estimating. — With these 
points decided, the problem remains of how to cover the area 
with the least possible cost. It is desired to obtain the total 
quantity of timber, by species, with a knowledge of sizes and 
quality. Cruisers of considerable experience in a restricted 
locality can size up timber by walking through it, and from their 
general knowledge of what similar stands have cut out, will 
make a guess at the total stand. This method is comparatively 
useless for large tracts, or with men of lesser experience or un- 
famiHar with a region, and is always subject to large errors. 

On the other hand, the cruiser may go to the trouble of meas- 
uring the contents of each tree separately. To justify this course 
the trees must be very valuable and the area small. Woodsmen 

* "Forest Mensuration," by Henry Solon Graves, Chap. Ill, pp. 27-35. John 
Wiley & Sons, Inc., N. Y., 1906. 



2 20 FOREST VALUATION 

almost invariably guess at the contents of the tree, either as 
a whole or by their knowledge of the contents of logs of cer- 
tain sizes. A better method is to use tables giving volumes in 
board feet, or in other units, for average trees of given diameters 
and heights, when such tables are available and are known to be 
reliable. 

219. Strip Methods. — By far the greater amount of timber 
estimating is done by methods involving the measurement of 
only a portion of the stand, in an effort to get an average which 
will apply to the whole area. Even if all the trees on a tract 
are observed, they may be merely counted, and an average 
volume obtained by guess or by tallying the sizes of a certain 
proportion of the stand. 

The most widely used methods consist of running parallel 
compass courses through the area at definite intervals, and meas- 
uring the trees standing on a strip of a definite width with the 
course as a center. In dense brush, or with small timber, this 
strip may be but 4 rods wide. Where tree callipers are used 
to get the diameter of each tree and the men employed to do 
the work have but Uttle experience in timber cruising, this 
width of 4 rods is seldom exceeded. More experienced woods- 
men, who estimate the timber by eye, usually cover a strip 
8 or 10 rods wide. The number and contents of the trees on 
these strips form the basis of the estimate. Should the strips 
so measured be accepted without question as giving an average 
stand for the whole area, the total estimate is found by using 
the multiple determined by the per cent of the area measured. 

220. Errors in These Methods. — But this is seldom the case. 
Timber is never uniformly distributed even over small areas, 
but varies enormously from acre to acre in size and density. 
Topographic and site factors exercise a marked influence on 
the stand. The timber tends to run in belts along stream 
bottoms and slopes. Chances of obtaining a better average 
are improved by arranging the strips to cross these belts, which 
object is most frequently attained by rurming up and down 
slopes rather than along them. 

For a given per cent of the total area estimated, the chances 



FIELD APPRAISALS OF TIMBER STUMPAGE 221 

for accuracy are improved in direct ratio to the size of the area 
units separately measured. Should the figures be desired by 
separate forty-acre tracts, an estimate covering lo per cent of 
the total would leave opportunities for large errors, while for 
a section of 640 acres, 10 per cent might give quite close results. 
Large and scattered timber requires a more complete estimate 
than small trees densely stocked. Very irregular or bunchy 
stands may require greatly increased work to arrive at a fair 
result. One method of dealing with this fundamental difficulty 
is to merely accept the result as within the allowable error for 
such work. Astonishing errors creep into timber estimates, 
even with experienced men. 

221. Types. — A second plan is to subdivide an area into types 
by means of a sketch map. In timber estimating, these type 
divisions are for the purpose of improving the possibility of 
getting a fair average stand. They are really stand classes. 
Blank or open areas are mapped and excluded in computing 
the total estimate. Only the area of strips run within a given 
type is used in determining the stand on that type. The amount 
of work which this method entails is somewhat greater than when 
the timber is calculated on the basis of the whole area, but this 
is often justified and the plan is used in a rough form by nearly 
all woodsmen. 

222. Correction Factor. — Another method of improving the 
final estimate without measuring every tree is the correction 
of the computed total, whenever the observations and judgment 
of the cruisers indicate its necessity. This correction must be 
based on actual inspection of the entire body of timber. When 
running strips, short side trips are made to view the timber which 
lies outside the strip. Should this timber run heavier or lighter 
than that measured, the total will be reduced or increased by an 
estimated per cent. This plan must not be confused with the 
method of guessing at the total stand, for it is based on a careful 
estimate, tree by tree, of a portion of the area. Should it be 
impossible for any reason to actually inspect the remaining 
timber, there can be no basis for correcting the result, which 
must stand for what it is worth. 



222 FOREST VALUATION 

223. Quality of Timber. — To judge of the quality of the 
timber, attempts have been made to grade logs, according to 
the relative value of their contents, into perhaps four classes. 
This is actually done in Puget Sound where a well-established 
log market exists and logs are purchased on the basis of the log 
grade or class. The difficulty with such a basis ordinarily is 
that logs vary in value from several sources; knots or sap in 
young timber, rot and wind shake in old trees. A dividing 
line or standard is not sufficiently definite, nor, except under 
the conditions cited above, are logs ever sold on this basis. 
They are paid for at a flat rate, according to the average value 
of the contents. The only recourse of the cruiser is to attempt 
to size up the quahty of the trees by their size, apparent age, 
clearness or freedom from knots, and soundness or freedom from 
interior defects. With a knowledge of the average per cent 
of grades produced in mills cutting similar timber, the cruiser 
estimates the per cent of each grade that the stand will cut. 
Should the timber be older, larger or better than the average 
stands, he increases his estimate of the higher grades to corre- 
spond. 

224. Reports. — The information which should be given in 
a satisfactory report on a tract of timber is shown under the 
following heads. 

I. Area. 

1. Description or location of specific tract. 

2. Area. 

3. Subdivisions of area. 

a. Blanks. 

Water. 

Barren. 

Burns. 

b. Reproduction or immature timber. 

c. Forest types. 

d. Age classes, where distinguishable. 



FIELD APPRAISALS OF TIMBER STUMPAGE 223 

II. Volume. 

1. Species: Separate estimates for conifers and 

hardwoods, and for each commercial species. 

2. Volume in merchantable units. 

a. Board feet. 

b. Cords. 

c. Pieces (poles, ties, etc.). 

3. Deductions from gross volume. 

a. Dead timber (probable durability). 

b. Cull, due to defects (rot, wind shake). 

III. Damage. 

1. Rot: Extent, character and amount of damage. 

2. Fire: Standing dead timber, damage to live 

timber, 

3. Insects: Location, prevalence, character of 

damage. 

4. Windfall: Location, amount and condition. 

rV. Quality. 

1. Size (if necessary, for two or more size classes). 

a. Average diameters, at 4^ feet (or at stump 

height) . 

b. Average heights. 

Number of merchantable i6-ft. logs. 
Total height of tree in feet. 

2. Form of bole. 

a. Straight or crooked. 

b. Taper, expressed in inches per i6-ft. log. 

c. Clear length. Limbs, character of knots. 

3. Grades. 

Per cent of probable output in each of several 
standard grades for species and locality. 

V. Young timber. 

1. Species. 

2. Area, in acres or in per cent of total area. 



224 FOREST VALUATION 

3. Average age. Range of ages. 

4. Sizes. Average and range of diameters and 

heights. 

5. Condition. Thrift, damage, with causes. 

6. Chances of survival. Competition with older 

timber, and with worthless species, or brush. 

7. Probable commercial value at maturity. 

VI. Soil. Quality. Agricultural value. 

VII. Logging conditions; summary for ^'logging chance^' 
rather than for each subdivision of estimate. 

1. Topography. By map or description. 
Character of slopes. Obstacles to logging. 

2. Surface. 

a. Underbrush. 

h. Rock. 

c. Character of bottom. 

3. Transportation. 

a. Streams, character for driving, cost of im- 
provements. 
h. Routes for roads, or railroad spurs. 
c. Methods of skidding and hauling. 

VIII. Modifications of logging required by silvicultural demands. 
Summary for logging chance. 

1. Amount and character of merchantable timber 

to be left standing. 

2. Methods of brush disposal, and precautions re- 

quired for protection of young timber (if not 
summed up for larger areas as a whole). 

IX. General conditions afifecting appraisal. 

1. Market value of lumber, or price basis. 

2. Size of mill, and cost of milling, with profits. 

Investment required. 

3. Cost of main transportation system. 



FIELD APPRAISALS OF TIMBER STUMPAGE 225 

X. specific conditions affecting appraisal. 

1. Specific costs of logging the "chance." 

2. Specific appraisal of value of standing timber 

per unit of log scale, based on total cost 
and total quantity, or distributed according 
to value of species (§ 180). 

XI. Appraised value of standing timber, by species, for 
specific units of product, modified for overrun to 
apply to standing timber. 



CHAPTER XV 

COMPARISON OF FOREST VALUES WITH AGRI- 
CULTURAL VALUES 

225. Agricultural Soils. — Agricultural soils are soils which 
will produce agricultural crops continuously in paying quan- 
tities, under proper cultivation and treatment. Many classes 
of soils will produce scant crops for short periods, after which 
they must be abandoned. Such soils should seldom be used 
for crops at all but kept under forest cover. Permanent agri- 
cultural fitness of soil is determined by six factors: quality of 
the soil itself, topography or slope, climate, water supply, the 
personal or human factor, and the economic factors. 

226. Quality of Soil. — Soils to be agricultural must be free 
from excessive quantities of rock, and not too sandy, since 
loose-textured soils will not retain sufficient moisture or soluble 
plant food to permit satisfactory growth. They should be 
underlaid by a permeable subsoil which permits sufficient drain- 
age. Deep sands, and stiff clay underlaid by hard-pan, are 
familiar types of non-agricultural lands. 

227. Slope. — The slope is important, since crops must be 
cultivated, and upon steep slopes, if not terraced, the loosened 
surface washes away, deep gullies are formed and the land is 
permanently ruined for agriculture. Slopes varying from lo to 
2o per cent, according to rainfall and quahty of soil, will prevent 
permanent cultivation. 

228. Climate. — Crops will grow in all but the coldest climates 
if given sufficient water. But in mountainous regions, lands 
at high elevations resemble regions near the arctic circle. Frosts 
occur every month in the year, and the growing of all agricul- 
tural crops, except a poor quality of hay, is prevented. Such 
lands are non-agricultural, regardless of the quahty of soil. 

226 



COMPARISON OF FOREST WITH AGRICULTURAL VALUES 227 

229. Water. — In regions of sufficient rainfall, low-lying 
lands are often swampy. Drainage transforms such soils into 
permanent agricultural lands of high value. In dry regions, 
irrigation brings otherwise desert soils under cultivation. Trees 
ordinarily require fully as much soil moisture as crops. Desert 
lands are therefore of no value for forestry, but undrained 
swamp land will produce valuable though slow-growing species. 

230. Personal Factors. — The personal element is a large 
factor in successful agriculture. Experience is the foremost 
need, but industry, economy and good business capacity are 
equally helpful. The advancement of agricultural knowledge 
by experiment stations, and the general trying out of new 
methods, often make success possible on soils and in climates 
which were once thought too hostile to permit of agricultural use. 

231. Economic Factors. — The development of transporta- 
tion, and increasing values for farm products, have a stimulating 
effect on agriculture, and farms can be made to pay in regions 
near large markets, which would be too poor to cultivate in less 
accessible locahties. This last factor, coupled with the advance 
in knowledge of farming methods, tends to bring more and more 
land into agricultural use, and the standard of classification 
between agriculture and forestry, for this reason, can never be 
a hard and fast one. 

But the differences between good and poor soil will remain 
as great as ever and some soil will always be too poor to farm. 
In densely populated eastern states sandy and rocky land in 
abundance is found, upon which the inhabitants eke out a mis- 
erable existence and which no amount of skillful management 
will make into profitable farms. 

232. Comparison of Agriculture with Forestry as a Source of 
Livelihood. — The use of land for the production of agricultural 
crops differs in many important particulars from its use for the 
production of timber crops. Agriculture, the direct source of all 
food supplies, )delds immediate livelihood to the farmer, whose 
returns are based on an annual cycle. A large element of labor 
enters into crop production, both for preparing and clearing the 
soil, and in actual cultivation and harvesting. Added to this is 



228 FOREST VALUATION 

the investment in buildings, fences, machinery and live stock- 
Agriculture requires large continuous outlays per acre, and in 
return must produce adequate income to compensate the farmer. 
If the soil is unsuited to agriculture, this outlay, which is as 
necessary on poor soil as on good, is inadequately rewarded, 
and the farmer impoverished. 

Trees grow best on good agricultural soils and produce their 
greatest values in such situations. But timber crops do not 
provide as stable a source of hvelihood as agriculture. The 
revenue from sales of timber is reahzed only after the lapse of 
the long period of growth. Mature stands may be sold or held 
at will and the income varied largely at the discretion of the 
owner as long as there are trees of suitable size for cutting. 

Over long periods, even at best, the net annual revenue from 
forest property is much lower than from agricultural crops. 
Relatively, forestry may be far the more profitable business. 
The expenses per acre are correspondingly lower than in agri- 
culture. While not giving a solid basis for continuous liveli- 
hood except in the business of lumbering, which requires large 
areas of land, forestry on the other hand does not require con- 
stant time and attention. Timber if given protection from fire 
will grow without cultivation. It therefore forms an ideal in- 
vestment for surplus income, but a poor basis for an individual 
living. 

The economic advantage of forestry over agriculture becomes 
evident only on poor agricultural soils. Trees of fair quaHty 
will still grow on soils utterly unfit for farming, and owing to the 
small expense attandent on this crop, will yield profitable returns 
on such soils. 

233. Non-agricultural Soils. — Since food and livelihood and 
permanent homes are more important to mankind than fuel 
and timber, soils which will repay the farmer should be devoted 
to farm crops. But the attempt to cultivate soils essentially 
non-agricultural leads to very serious results both for the indi- 
vidual and for society. Soils are non-agricultural when they 
cannot continue year after year, with proper care, to produce 
paying crops. Non-agricultural soils, when cultivated, either 



COMPARISON OF FOREST WITH AGRICULTURAL VALUES 229 

wash away by erosion, blow into sand dunes, lose their small 
store of fertility by too active drainage, or for other reasons fail 
to respond to the efforts of the farmer. 

234. Exploitation of Land Purchasers. — Intelligent farmers 
refuse to buy or work such lands. Uninformed purchasers, 
either foreigners or city emigrants unused to farming, buy 
these lands because they are cheap. They are even less able to 
make a Hving upon them than are the more experienced farmers 
who have passed them by. The effort results in financial and 
often in moral bankruptcy. Lands of this character thus change 
hands often, and since the real estate business is based on land 
transfers, it thrives on such conditions. 

Whatever hurts the individual hurts the whole community. 
The exploitation of well-meaning land-hungry investors by 
professional land locators and real estate sharks is a business 
closely akin to more pronounced forms of swindling. Local 
sentiment in such communities will be largely molded by these 
selfish predatory interests and will resist attempts to properly 
classify such land as non-agricultural. Thus a condition is 
created containing hmitless possibiHties of evil to the pubHc at 
large. 

235. Land Classification. — The solution of this problem Hes 
in the scientific classification of lands, to determine whether or 
not agriculture is possible. If unsuitable for farms, then the 
lands fall naturally into the class of forest soils, and should be 
removed from the market as agricultural land, and devoted to 
forest production. The best way to accomplish this removal is 
for the states to purchase such soils for forest reserves or for the 
national government to acquire them for stream protection. 

236. Basis of Comparison of Agricultural and Forest Values of 
Land. — To compare the value of land for agriculture with its 
value for forestry, each value must if possible be expressed in 
money. In each case the basis of value is future net income 
capitahzed (§62). If we include for hothouses all items of future 
income, minus future costs, and can appraise this income and its 
present value accurately, the comparison will reveal the relative 
value of the property and determine whether the soil is best suited 



230 FOREST VALUATION 

to farming or forestry. Unfortunately, the uncertainties affect- 
ing the determination of these future items, in both cases, prevent 
a satisfactory mathematical comparison of such values. Yet 
whatever the basis on which the comparison is made, it is 
founded on the economic relations which such calculations set 
forth. 

237. Expectation Value of Agricultural Land. — The basis 
of agricultural value is the net revenue from crops. The actual 
cost of labor and use of machinery is deducted from the sale 
value of the crops and the average net return is capitalized. 
Owing to the fact that on small farms the proprietor puts in 
his own labor and raises food for his family, this net income is 
not often accurately computed. Cash rent paid for farm land 
separates the costs from the income, since the tenant presumably 
gets only his just share, including profit, and the rent represents 
the net income earned by the soil. Since this is annual, it is 

capitalized by the formula (XII) , on the basis that the 

o.op 

farm will produce this rental without deteriorating. A farm 

earning $5 per acre rent will, at 5 per cent, be worth $100 per 

acre. 

238. Sale Value of Agricultural Land. — Improved farm 
land is transferred with sufficient frequency to establish sale 
values, in any region where farming is a well-developed industry. 
These sale values will, on the whole, coincide quite closely with 
the capital or appraised values of farms based on net income. 
But traditions, demand, and increasing or declining population 
affect farm values and prices to a great extent. Values of farm 
property are sluggish at times and again, in boom periods, out- 
strip conservative appraisals of income. In this the human 
element in price making is seen to play a large part (§§17, 

59, 69.) 

239. Timber as an " Agricultural " Value. — Improved farm 
land is not the true basis of comparison with forest land. 
Land in its wild state ranges from heavily timbered tracts 
through all degrees of stocking and of young timber, to natural 
prairies needing only to be broken for a crop. Land which 



COMPARISON OF FOREST WITH AGRICULTURAL VALUES 23 1 

has been stripped of timber, but is covered with stumps which 
interfere with the cultivation of the surface and prevent the use 
of machinery, is the condition in which the prospective farmer 
in most cases has to accept property in timber regions to-day. 
In former times, timber itself had no value, hence the cost 
of removing it, including the burning of the logs, gave such 
lands a low initial value. It is still necessary to cut and remove 
standing timber from agricultural soils, but the timber now has 
a stumpage value and its removal will cost the owner nothing, 
while its sale supphes him with capital with which he can un- 
dertake the work of clearing the land of stumps. The presence 
of merchantable timber upon such soils thus aids, apparently, 
in establishing agricultural use. 

In heavily timbered regions, this seldom works out. Stump- 
age cannot be marketed at will and in many regions must await 
the slow development of transportation and the gradual cutting of 
the more accessible timber. The owner cannot afford to sacrifice 
it for agriculture, except on a small portion of the area and, 
consequently, sells this land with its timber to some lumber 
company. In time, the land is stripped of timber and the 
stump land is offered to purchasers for agricultural use. 

Timber values on agricultural soils cannot be regarded in any 
sense as agricultural values, but are the equivalent of so much 
money capital to the owner of the land. Granting that pur- 
chasers who secure timber obtain more valuable property than 
those who get only stump land, it is still evident that the agri- 
cultural value of forest land must be based solely on the land 
bare of all timber. 

240. Stump Land versus Cleared Land. — The value of 
stump land is less than that of open meadow or prairie land 
in its wild state, by the amount of the extra cost of clearing and 
preparing it for cultivation. The crops are the only source of 
value, and since improved land is now bearing crops its value 
rests on a firm basis. Between this value and that of stump land 
is interposed the future costs of clearing and breaking, and the 
time necessary to do the work. Fencing, development of water, 
and buildings must be added, before agriculture can be sue- 



232 FOREST VALUATION 

cessful. These future costs depress the real value of stump 
land, and cause a wide divergence between the true values of 
wild land and improved farms. 

241. Cost of Clearing Stump Lands. — The appraisal of the 
cost of clearing land is not difficult, but if based on the actual 
cost of wages for the labor required in clearing up ground at 
one operation, it is apt to be too high. Land is seldom cleared 
in that way, except by land companies supplied with large 
capital. The settler clears gradually, using his own labor at 
slack seasons, cultivating between the stumps, grazing the 
land, and allowing the stumps to rot. The roots of hardwood 
and sap pine stumps decay in from three to ten years and the 
stumps are easily gotten out. The stumps of heart pine and 
certain other conifers do not rot readily but will pull much more 
easily after a few years than at first. The loss in time is great, 
since the full utility of the soil for crops is not attained for years. 
The settler may even be investing an amount of labor and capital 
in the clearing for which, judged commercially, he will never 
be repaid. But clearing will be attempted successfully even on 
lands on which its cost apparently exceeds the final value of 
the land. Therefore the cost of clearing, provided the soil is 
good, should not be regarded as indicating a negative expectation 
value for stump land. Should the cost exceed the value of 
cleared land, a very low value for stump land is indicated, but 
this value will still be positive in most cases. 

242. Sale Value of Stump Lands. — Sale values for stump 
lands are often falsely or inaccurately determined and are set 
at far too high a figure. This is due to the lack of general 
knowledge of the costs and delays of clearing. The values for 
highly productive improved lands, perhaps bearing orchards, 
are compared with stump lands, to the enhancement of value 
for the latter in the minds of purchasers, many of whom 
know nothing of the problems involved. It is safe to say that 
without the necessary additional capital to hire the clearing 
done, such lands can never be developed by this class of inves- 
tors out of the income from the property, while persons of 
small means cannot buy stump land at high initial prices and ever 



COMPARISON OF FOREST WITH AGRICULTURAL VALUES 233 

expect to lift the mortgages which they must usually accept. 
In contrast to boom sale values upon such lands, the appraised 
value of stump land should be reasonably low compared with 
improved tracts in the same neighborhood. 

243. Summary of Elements of Value for Forest Land. — The 
elements of value which must be considered in arriving at the 
value of forest lands are: 

Value of mature or merchantable timber. 
Expectation value of young timber. 
Value of land based on future timber crops. 
To these values must be added: 

Value of improvements as roads, fire lines. 
Value of protective influence of the forest. 

The determination of value for merchantable timber is dis- 
cussed in Chapter X. Actual prices received for similar timber 
are commonly accepted as indicating this value. 

The value of young timber and of land is found by the methods 
described in Chapter VI, when an appraisal is necessary. 

Roads and other improvements do not influence value on 
the basis of what they cost, but by their effect in cheapening 
transportation, lowering fire risks and increasing the net income 
or lowering the rate of interest (§§211 and 68) . In proof of this 
statement it is recognized that in agricultural appraisals the cost 
of dwellings and other improvements on farms is not the basis 
on which the farm is valued, although they add to its value by 
providing the immediate facilities for deriving the income by 
cultivation. 

The value of the protective influence has been discussed in 
Chapter VII (§ 146). This value benefits adjoining property 
rather than the land itself, but is an important factor when 
weighing the relative merits of agricultural versus forest use. 
Fortunately, slopes valuable for their protective forest cover 
are usually too steep to be tilled without inducing erosion, and 
the demonstration of this fact would at once prevent the 
classification of such soils as agricultural by an intelligent 
investigator. 



234 FOREST VALUATION 

Of these five items of value only the revenue from sale of 
mature timber is immediately available. This is comparable 
with the revenue from the current crop on agricultural land. 
When ready to harvest, it greatly exceeds the latter as it rep- 
resents a long accumulation. 

244. Value of Young Timber as a Part of the Value of Forest 
Soil. — When comparing the value of land for forestry with 
agricultural values, we assume that the land has some value 
for agriculture. Absolute forest soils, whose agricultural use is 
impossible, need not be valued in order to determine the class 
to which they belong. 

Where agriculture is possible, but its profitableness is ques- 
tionable, and the cost of clearing is high, the value of the land 
for forestry may greatly exceed any value for farming. Here 
a calculation of forest values will be of great assistance in deter- 
mining the best disposition of the land. 

Agricultural soil is always regarded as bare land and the value 
as that of the soil itself, not including crops which may be grow- 
ing. This is merely because of the short crop period. In 
reality the standing crop increases the value of the property 
while present and is the source of this value, and a purchaser of 
the land must either permit the former owner to harvest the 
crop or pay him for it. Forest land to be compared with agri- 
cultural land on the same basis must be bare of timber. But 
it is the timber crop that gives the land whatever forest value 
it has (§ ii6). In actual practice, forest land is seldom in this 
bare condition. As seen in Chapter VII, the actual value of 
forest property depends upon the closeness of the date of realiz- 
ing the income from the timber. The value of the timber may 
be separated from land if necessary, but this separation is arti- 
ficial (§ 135). The real value of forest property is based on the 
actual condition of the stand, its age and size. Forest values 
differ from agricultural values in that they fluctuate over long 
periods with the growth and removal of the crops instead of 
maintaining a reasonably constant relation from year to year. 
The lowest ebb is represented by bare land, and in a system of 
clear cutting this condition is attained but once in the period of 



COMPARISON OF FOREST WITH AGRICULTURAL VALUES 235 

growth of the crop, just previous to planting. In any system 
of natural seeding, and especially with selection cutting, the value 
of forest "land" never reaches this low point, but is maintained 
at a higher level by the presence of partly grown timber which 
will bring in revenue in a shorter period than a full crop 
rotation. 

If young timber is present on forest soils, it is not possible 
to consider this timber as having no value without rejecting the 
basis of all values, which is future income. We cannot consider 
merely the forest value of the land itself, for this is derived 
wholly from timber. The expectation value of the young 
timber is more definite than the same value calculated for the 
soil itself (§ 116), as it is nearer and more certain than that from 
non-existent future crops, or ''soil." If land bearing young 
timber is cleared for agriculture, the forest value sacrificed is 
greater than that of forest land by just the difference that the 
age of this timber makes in the present value of the income 
expected from it. To ignore this value would be the same as to 
consider a half grown crop of wheat as adding nothing to the 
sale value of agricultural land. 

Nor can we ignore the future income from young timber as 
an element of forest value on the grounds that this is not a 
present but a future value, perhaps not attainable for several 
decades. If agricultural values were based merely on the revenue 
from the next year or decade, the capital value of farm land 
would be much lower than it is. All future revenue is included 
in such agricultural values as surely as it must be included in 
finding the present value of forest property (§85). The mere 
fact that forest income is irregular makes it no less necessary to 
value the entire future income in finding the value of the prop- 
erty for forestry. 

245. Sale Value of Forest Property. — As in the case of 
agricultural soils, sales are the generally recognized basis of 
value for forest property, soil and standing crops included. 
But the sale value of forest property may suffer from ignorance 
or lack of recognition of the true worth of the property (§111). 
If young timber has been allowed to burn up in the past, or if 



236 FOREST VALUATION 

insufficient time has elapsed since logging began on the virgin 
forest, the fact that young timber will grow into a valuable 
merchantable stand, or second growth, is not generally appreci- 
ated. The forester, a specialist on appraisal of growing timber, 
can estimate this value on its true basis. But the public will 
place a much lower estimate on the property, or may ignore 
altogether the element represented by the young timber and 
value the land itself on an arbitrary basis not related to its 
use for forest production, but based on grazing or other uses. 

Purchasers of land follow a sound policy in acquiring it at as 
low a value as possible, and if bought for forestry they gain 
by this condition of undeveloped sale values. But as a basis for 
classification, the acceptance of existing sale values of land and 
young timber, merely because the public are not familiar with 
true values, is wholly inexcusable. When this condition is 
further aggravated by accepting an inflated agricultural value 
for unimproved stump lands, the comparison is unfavorable to 
the securing of a true and lasting classification. 

246. Discrimination against Forest Values. — Where eco- 
nomic pressure is strong for the listing and opening of lands for 
new settlers, the tendency is to deliberately ignore the expec- 
tation value of young timber as well as of the land, and to con- 
sider only the mature timber as indicating the sum of forest 
values. Or, perhaps, the forest value of the land is recognized, 
but not that of young trees. This is even more inconsistent 
than the first plan. The argument is advanced that the value 
of young timber will not be realized for many years while that 
of agricultural crops applies to the present moment. But if 
these timber values are based on present stumpage prices (§195) 
and properly discounted to the present, it must be evident from 
the discussion in Chapter VI that expectation value is a true 
present value, strictly comparable with that for agriculture 
(§ 244) . Rejection of such appraisal can be justified only in two 
ways, — when forest values are actually less than agricultural 
values for stump land, or on the basis of poHtical expediency. 

247. Discrimination in Favor of Forest Values. — The rec- 
ognition of increasing future prices brings an element of specu- 



COMPARISON OF FOREST WITH AGRICULTURAL VALUES 237 

lation into such appraisals, and when this is done, the present 
values thus found are no longer based on present but on future 
conditions. It is this element, and not the discounting of future 
income to the present, which would unfairly alter the basis of 
appraisal in favor of forest values. A parallel case would be 
found were it estimated that prices for farm crops would in- 
crease and that the value of land at present should be based on 
an appraisal of this future increase in annual income. 

Future growth in volume is a justifiable assumption, as is 
also an improvement in quality of timber and of unit price based 
on this quahty, to conform to the higher prices now received for 
similar grades (§§ 183, 184). But the discounting of future in- 
creases in the general price level for timber is as little justified 
in the case of valuation for comparison with agriculture as it is 
in valuing damages to young timber. In either case, present 
values must be based on present prices, and future increases may 
be used only by the owner in computing possible or speculative 
profits. 

248. Results, when Values of Bare Land are Compared. — 
From the above discussion it is assumed that a true comparison 
of forest with agricultural values is based on a computation or 
appraisal of the expectation or present capital value of the 
property for each use, the forest values present in the form of 
timber and land being compared with the value of stump land 
for agriculture. The highest value for both purposes will always 
be found on the richest agricultural soils. But it will seldom 
if ever be true that the forest value of bare soil will exceed its 
agricultural value if the soil is fairly adapted to crop production. 
Only upon the poorer or non-agricultural soils will land itself, 
even at a low forest value, be worth more for wood crops than 
for agriculture. 

249. Results, when Full Value of Property is used in 
Comparison. — With the growth of the timber, however, a 
corresponding increase takes place in the forest values of the 
property or "land," until at some point during this growth the 
actual present value of the timber and land exceeds the agri- 
cultural values. At any time previous to this, it is justifiable 



238 FOREST VALUATION 

to destroy the young timber and clear the land, although in doing 
so a greater value is sacrificed or wasted than if stump land only 
were so used. The destruction of merchantable timber in 
former days was justified on this basis, since the value of the 
land for agriculture exceeded the total timber values present. 

But pioneer conditions have passed, and the destruction of 
merchantable timber values is no longer thought of except 
where these pioneer conditions are reproduced by lack of trans- 
portation and markets. Even as the former settlers found 
that with increasing values the uncleared portions of the farm 
became a source of unexpected wealth, so in the future it will 
pay the settler to protect young growth and keep a portion of 
his farm in timber. 

The mature timber upon agricultural land adds a forest value 
to the value of the stump land. The land is worth just as 
much more to the settler as the price he can get for his standing 
timber. The only drawback is that until this is sold and re- 
moved he cannot begin his clearing. But upon most claims there 
is enough poorly timbered soil to occupy the time and energies 
of the settlers until such sale is effected. Should there be no 
such openings, and the entire claim be heavily timbered, agri- 
cultural use is inevitably postponed until logging commences, 
for the relative value of the timber is so great as to preclude 
any other course. 

250. National Forest Policy in Land Classification. — - In 
classifying national forest land in pursuance of the policy of 
granting homesteads, land should not be listed for settlement 
while the total forest values exceed the agricultural value of 
stump land. This necessitates the sale and removal of mature 
timber from agricultural soils, previous to listing. But owing 
to the pressure for land throughout the west the tendency is 
at present to ignore the appraised value of immature timber 
and even the capital value of forest land, and to permit the 
listing of lands containing a certain amount of merchantable 
timber. This reservation is beneficial to the settler for it gives 
him a subsidy or value in addition to his land. 

Since this procedure clearly sacrifices all forest values except 



COMPARISON OF FOREST WITH AGRICULTURAL VALUES 239 

the present saleable timber, it will inevitably result in listing 
rapidly all lands of agricultural value whether or not they are 
covered with young trees, provided only that the merchantable 
stand is not too dense or valuable. If this policy is demanded 
by dearth of farm land in these regions it should be carried out, 
but the basis upon which the classification is made must be 
frankly recognized as expediency rather than sound appraisals 
of value. 

251. Reciprocal Values in Forestry and Agriculture. — Forest 
and agricultural values cannot be considered as wholly sepa- 
rate. On every agricultural unit there is need of a certain 
amount of forest land to furnish wood for fuel, fence posts and 
even lumber, and as shelter for stock and windbreaks. In 
treeless prairies the planted grove greatly enhances the desira- 
bility of the whole property as a residence and adds in this way 
far more to the sale value of the farm than is accounted for 
by the possible revenue which this grove could produce. In 
wooded regions the labor of clearing is so great that two or even 
three decades must elapse before the entire farm will be brought 
under cultivation by the efforts of the farmer, unless aided by 
investing the necessary capital in clearing on a large scale. 
Meanwhile the woodlots will grow at an appreciable rate and 
young timber at first but a few feet tall will become large 
enough for use. In many regions this wooded portion may also 
be grazed without undue injury to the trees, if the latter have 
sufi&cient height. 

Every effort should be made by owners of such tracts to spare 
and encourage areas of reproduction and of young timber, more 
especially when such growth occurs on the poorer portions, 
steeper slopes and more inaccessible parts of the farm. In 
this way each part of the farm unit is put to its best use, the 
maximum returns are obtained, and the sale value of the entire 
property will usually exceed the sum of the forest and agricul- 
tural values when separately considered. 



APPENDIX 

Formulae. 

Summary of Formulag of Compound Interest. 

Definitions of Symbols. 

Summary of Formulae of Forest Valuations. 
Compound Interest Tables (Table VI). 
Tables of Logarithms (Table VII). 

SUMMARY OF FORMUL.S: OF COMPOUND INTEREST 



Character of payments. 



Single sums. 



Temporary rentals, 
annual 



intermittent . . 



Perpetual rentals, 
intermittent 



annual 



Values at the end, future 
values, cost. 



FoX i.o/>" 



(I) 



r (i.o/>"- i) 



o.op 
r'(i.op"«- i) 



I .op" - I 
r'(i.o/)"'-i) i.op^' 



I .op" — I 



(HI) 

(V) 
(VII) 



o.op (i.op") 
r'(i.op"'- i) 



Values at the beginning, present 
values, capitalized income, capi- 
tal value, expectation value. 



Vn 



I. op" 



(H) 



r (i.op"- i) 



(i.op"- i) i.op"« 



(IV) 
(VI) 



'^^'f-^^'tr (VIII) 



(i.op" - i) i.op 



I. op"- I 
r' (i.op"-°) 



i.op"- I 
r'd.op") 



I.op"- I 

r 
o.op 



(IX) 

(X) 

(XI) 

(XII) 



r' 

Conversion of intermittent into annual rentals, — X o.op (XIII) 

I.op — I 



Ratio of income to capital investment, :x; = loo 



(v/^:-) 



(XIV) 



240 



APPENDIX 




241 


SUPPLEMENTARY FORMULA 






-^ (i.o/?« - i) I I.op" + -^ ii.op"- 
o.op ) o.op 


i). 


(Ilia) 


R{i.op''-i). 




(Illb) 


/(i.o/>") 
I.op" — I 




(Xa) 


„, . r' 




rvTa^ 



I.Oj^" — I 

DEFINITIONS OF SYMBOLS 
a — Year, previous to n, for which value or cost of property 
is sought. 

J — ^-^^ ~ ^ ^ ratio used in Formulae P3 and P4 in deter- 
o.op 

mining the amount (Z) to be written off annually 

for profit and depreciation. 

e — Annual expenses, constituting one year's net outlay. 

g — First term of a geometric series. 

m — Interval between intermittent yields in a many-aged 
forest. 

n — Period required to produce a crop of timber. Rotation. 
Interval between yields produced by even-aged stands 
of timber. 

p — Standard rate of interest in forestry. 

q — Ratio, or multiple, for a geometric series. 
g% — Per cent of legitimate profit to be allowed in logging 
and milling, or in logging alone, in stumpage ap- 
praisals. 

r — Annual rental, regarded either as income or outlay. 

/ — Intermittent rental, due at regular intervals greater 
than one year. 
r% — Per cent of legitimate profit to be allowed in milling 
alone, in stumpage appraisals. 

5 — Per cent of overrun per thousand board feet, log scale. 

/ — Number of payments expected in a temporary inter- 
mittent rental. 



242 APPENDIX 

X — Rate of dividends or interest earned by an investment. 

z — Per cent of value to be written off annually for depre- 
ciation in Formula P2. 

A — Original capital investment in assets subject to depre- 
ciation. 

C — Cost of initial silvicultural and protective measures, 
incurred in first year. 
Cd, Ce, Cf — Cost of silvicultural and protective measures, 
incurred in subsequent years, d, e and /. 

D — Total amount to be written off for depreciation during 
the life of an enterprise. 

E — Expectation or capital value of annual expenses, e, 

by Formula XII, • 

"Fc — Total cost of forest property, including both land and 
growing stock or timber, for the year a. For year n, 
substitute "F^ or F^. 
Fg — Sale value of forest property, both land and timber, in 

the year n or when timber is mature. 
"Fg — Expectation value of this sale value for the year a, 

previous to the year n or year of sale. 
Fy — Expectation value (capital value) of forest property, 
including both land and timber. Applicable to both 
even-aged and many-aged stands. 
"F^ — Expectation value of forest property for year a pre- 
vious to year n. 
Gc — Cost of growing stock or standing timber. 
"Gy — Expectation value of growing stock, or standing timber, 
separate from land, for the year a previous to year n. 
L — Total amount of loss or damages to forest property. 
LC — Logging costs. 

LD — Depreciation of logging investments. 
MC — Milling costs. 
MD — Depreciation of milling investments. 

P — Profit or enterpriser's gain, remaining after paying 

interest at p per cent on capital investment. 
Q — Sum of terms in a geometric series. 



APPENDIX 243 

R — Expectation or capital value of the sum of payments 

constituting a rental. 
5 — Sale value of lumber or of logs. Value of soil. 
Sc — Cost of soil and of permanent improvements. 
Ss — Sale value of soil. 

Sv — Expectation or capital value of forest soil. 
Tp, Tq, Tr — Net income from sale of thinnings in years p, 
q and r. 

V — Value of a single sum. 

Vo — Value of sum at beginning of period. 

Va — Future value in year a of the sum of items of income 

and expense on a crop of timber. 
Vn — Value of a single sum at end of a period of n years. 
Vr — Future value of the sum of payments constituting a 

rental. 
W — Final, wrecking or residual value of assets in logging 

or milling, after writing off total depreciation. 
X — Annual sum required to be written off for depreciation. 

Y — Sale value, or appraised value, of timber stumpage. 
F' — Sale value, or appraised value, of timber stumpage, 

resulting from fire or other damage. 
Ym — Stumpage value of 1000 board feet of manufactured 

lumber, used as basis to determine Y. 
Z — Annual sum which combines income or profit on in- 
vested capital with depreciation, the sum constitut- 
ing one of a series of equal annual payments. 

SUMMARY OF FORMUL.E IN FOREST VALUATION 

Costs 
Cost of a single even-aged stand of timber. 

Index Art. 
Letter 

Gc={C-\-Sc-{-E)i.op-- (Sc + E) .... A 105 

+ Q(i.op-0 - Tp (i.op-^) - Tqii.op--'^) 

-Tr{i.op^-') -{Sc-^E) Ai 105 

Cost of a forest, including timber and soil, for year a. 

"F, = {C + S, + E)i.op'^ - E ...... A2 105 



244 



APPENDIX 



Cost of a normal many-aged forest. 



Index Art. 
Letter 



Gc = 



{C-{-Sc + E)(i.op^- i) 
o.op 



— n{Sc-\- E), . A3 109 



Values 

Sale value of a single even-aged stand in year n, in- 
cluding value of soil. 

F,= Y-hS, B 112 

Expectation or capital value of above for year a, pre- 
vious to year n. 

Y + Ss-\-E 



"i^, = 



"F. = 



-E. 



Bi 112 



i.o^"-" 

Y-\- 5,4- E +T^{i.op^-^)+ T.ii.op^-") 
+Tr{..opr^-) ^^B^ ^^^ 



Expectation or capital value of forest property in 
the year n, previous to removal of crop. 
Y -C 



F. = F-f 



I.O^" —I 



F^ = Y-{C+E) + 



(CH-£) C 

fF-f Tp (i.op-^) + T,{i.op--<^) 
+ r.(i.o^"-0-C-Cd(i.oi>"-<^) 



i.o/?" - I 

Expectation or capital value of forest property in 
the year a, previous to year n. 

ap^ ^jy-c) i.or _ E D 

I. op'' — I 

i.opp i.op" I. op' 

c,(i.or) _ c(i.or) _ Q(i.or) 

i.op'^ i.op" i.op^ 



114 



114 



115 



ap _ 



I. op" 

-E. Di 115 



i.o^" — I 
ap Y + S. + E _^ D2 116 



APPENDIX 245 

Index Art. 
Letter 

Expectation or capital value of forest soil. 

S,= ^~^ -{C + E) E 116 

I. op" — I 

IY+Tp{i .op"-^) + r, (i .o/>»-') + Tr (i .or-O 
o ^ l-C-C,(i.o/>"-^)-Ce(i.o/>--)-Q(i.o/>"-0 _ 

I.O/>" - I \ ^ ) 

El 116 
Soil rent = 5„ X o.o/> E2 116 

Expectation or capital value of a many-aged forest 
in year m, just subsequent to removal of crop. 

F.= ^"^ -(C + £) F 117 

i.o/>" — I 

Expectation or capital value of a many-aged forest 
in year a, previous to year m. 

Y + F, + E _^ F, „^ 

I. Op""-" 

Expectation or capital value of a many-aged forest 
producing annual income. 

t^ = 7 r2 117 

o.op 

Expectation or capital value of a many-aged forest 
for irregular yields and periods. 

V—C V—C V—C 

^—^ (i.or-") + ^^—^ (i.op^-') + ^—^ {i.op"-') 

F^=- '-Tn ^ 

i.o_p" — I 

F3 118 

Expectation or capital value of growing stock or 
timber separate from soil, in year a, previous to 
year n, for a single even-aged stand. 

°G,= ^ + f:+^ -(5.-i-£) G 119 



246 APPENDIX 

Index Art. 
Letter 
Expectation or capital value of growing stock or 

timber separate from soil, in year a, previous to 

year m, for a many-aged stand. 

°g. = ^ "^ ^1^„ ^ -(S^-h E) Gi 119 

I. op 

Profits 

Profits in destructive lumbering, on timber and land, 

for year n or at time of sale of timber. 

P ^Y -\-S, + E- {C + Sc-\-E)i.op- . . . H 122 

P = F + 5, + £ + r, {i.op^-^) + T, {i.of^-") 

+ Tr {i.op--') - (C + 5o + £) i.op'^ 

- Cd (i.o/)"-'') - Ce (i.o^"-^) - Q (i.o/>"-0- Hi 122 

Profits in destructive lumbering, on timber alone, for 

year n. 

P=Y -\-Sc-{-E-{C-\-Sc + E)i.op\ . . . K 123 

Profits in destructive lumbering, on timber alone, for 

year a, previous to year n. 

P = -^ "^ ^^ "^ ^ - (C + 5c + £) i.o/>°. . . . Ki 124 
I .op"'" 



P = ' ^ ' + -^^^ + ^^— + 

I. op"-" I. op''-'' I. op"-" LOp'-" 

- (C + 5c + £) i.or - Q (i.or-') 

. -Ceii.op'^-') -Cf{i.op''-0 K2 124 

Profits in continuous forest production, for year n. 

p = F + 5„ + £- (C + 5c + £) i.or. . . . L 125 
Profits in continuous forest production, for year a, 
previous to year n. 

P = ^ "^ ^" + ^ - (C + 5c + £) i.o/>° ■ . . Li 126 
I. op"-" 

P = -F^-"Fc L2 126 

P = (5, - 5,) i.op" L4 126 

Profits in continuous forest production for year o, 
previous to origin of crop. 

P = S,-Sc L3 127 



APPENDIX 247 

Index Art. 
Letter 

Interest Earned 
Rate of interest earned on soil capital. 

1.00;'* = ^^ ~ N 129 

Rate of mterest earned on soil and initial investments. 

7 + 5, + £-£(i.o/>") ,^ 

^.ox-= ^ .Q — Ni 129 

Rate of interest earned on entire investment. 

F + 5, + £ . . 

^•-^" = 5. + C + E ^^ ^^9 

Mean annual forest per cent. 

x = ^X p N3 129 



Current annual forest per cent. 

F„+i - F„. - e 



X = ( "+^ " — -j 100 N4 129 

Current annual forest per cent, for normal forest. 

X =-^ Xp Ne 129 

Fc 

Damages 
Damages to mature timber. 

L=Y-Y' O 140 

Damages to young timber for year a, previous to 
year n. 

T Y -Y' ^ 

L = Oi 141 

i.o/>"-" 

Damages to timber and soil, for year a. 

£,= ll±AJl^_j_C' + £'- (C + £). . . . O2 142 
i.o/>"-" 



248 APPENDIX 

Index Art. 
Letter 

Depreciation 
Depreciation, Method A. 

X = -^^5:5£i p 

I.O^" — I '^ 

Depreciation, Method B. 

^ D A-W ^ 

X = - = Pi 175 

n n 

Depreciation, Method C. 

z=ioo^i-yjj P2 17s 

Depreciation, Method D. 

z = ^ (i.°r) - w p^ 

a 

Z= ^ (0.0/)) 4- —(Hunter's formula). . . . P4 175 
a 

Geometric Series 
Sum of rentals, increasing temporary series. 

Q^sjT:^ Q^ 80 

q- I 
Sum of rentals, decreasing temporary series. 

Q^Sjl^LTl Q^ 80 

I -q 
Sum of rentals, increasing perpetual series. 

(2 = 00 Q3 80 

Sum of rentals, decreasing perpetual series. 

Q = — ^— Q4 80 

I -q 



APPENDIX 249 

Index Art. 
Letter 

Stump AGE Values 

Stumpage appraisal on basis of manufactured lumber; 
profits, a per cent of operating costs. 

Y,n=S-{LC+MC + D)-q%{LC^MC-\-D) R 177 

Ym = S -{MC+MD+LC+LD) -r%{MC+MD) 

-q%{LC + LD) Ri 177 

Stumpage appraisal on basis of manufactured lumber; 
profits, a per cent of sale value. 

Ym = — ^^ {LC + MC + D) R2 177 

I +q% 

Stumpage appraisal on basis of manufactured lumber; 
profits, a per cent of margin between operating costs 
and sale value. 

Ym = q%\S-{LC + MC + D)\ R3 177 

Stumpage appraisal on basis of manufactured lumber; 
reduction to log scale. 

F= Yr.ii.os) R4 179 

TABLE VI 
COMPOUND INTEREST TABLES 

The period, n years, in left-hand column. 

Column I, Formula I. — Future value of $1 at end of n years. 

Column II, Formula II. — Present, expectation or capital value of $1 due in n 

years. 
Column III, Formula III. — Future value at end of n years of an annual rental 

of $1 payable n times. 
Column IV, Formula IV. — Present, expectation or capital value of an annual 

rental of $1 payable n times. 



250 



APPENDIX 





i PER CENT 




n years. 


I. 


II. 


III. 


IV. 


1 


1.0050 


9950 


I. 0000 


• 9950 


2 


I. 0100 


9901 


2 . 0050 


I. 9851 


3 


1.0151 


.9851 


3.0150 


2.9702 


4 


1.0202 


9802 


4 ■ 0301 


3-9505 


6 


I 0253 


9754 


5-0503 


49259 


6 


1.0304 


9705 


6-0755 


5-8964 


7 


I -0355 


9657 


7 • 1059 


6.8621 


8 


I .0407 


9609 


8.1414 


7-8230 


9 


I -0459 


9561 


9.1821 


8.7791 


10 


I. 05 I I 


9513 


10.2280 


9-7304 


11 


1.0564 


9466 


11.2792 


10.6770 


12 


I .0617 


9419 


12.3356 


11.6189 


13 


I .0670 


9372 


13-3972 


12.5562 


14 


1.0723 


9326 


14.4642 


13-4887 


15 


1.0777 


9279 


IS -5365 


14.4166 


16 


I. 0831 


9233 


16.6142 


15-3399 


17 


1.0885 


9187 


17.6973 


16.2586 


18 


I -0939 


9141 


18.7858 


17.1728 


19 


1.0994 


9096 


19.8797 


18.0824 


20 


I . 1049 


9051 


20.9791 


18.9874 


21 


I. I 104 


9006 


22.0840 


19.8880 


22 


I . I 160 


8961 


23.1944 


20.7841 


23 


1.1216 


8916 


24.3104 


21.6756 


24 


I. 1272 


8872 


25-4320 


22.5629 


25 


I. 1328 


8828 


26.5591 


23 4456 


26 


I. 1385 


8784 


27.6919 


24.3240 


27 


I. 1442 


8740 


28.8304 


25.1980 


28 


I . 1499 


8697 


29-9745 


26.0677 


29 


1-1556 


8653 


31.1244 


26.9330 


30 


1.1614 


8610 


32.2800 


27.7941 


31 


I .1672 


8567 


33-4414 


28.6508 


32 


I. 1730 


8525 


34 . 6086 


29-5033 


33 


I. 1789 


8482 


35-7817 


30.3515 


34 


I. 1848 


8440 


36 . 9606 


31.1955 


35 


I . 1907 


8398 


38-1454 


32.0354 


36 


I. 1967 


8356 


39-3361 


32.8710 


37 


1.2027 


831S 


40.5328 


33-7025 


38 


1.2087 


8274 


41-7354 


34-5299 


39 


I. 2147 


8232 


42.9441 


35-3531 


40 


1.2208 


8191 


44-1588 


36.1722 


41 


I .2269 


8151 


45 3796 


36.9873 


42 


1.2330 


8110 


46 . 6065 


37.7983 


43 


1.2392 


8070 


47-8306 


38.6053 


44 


1.2454 


8030 


49.0788 


39.4082 


45 


I. 2516 


7990 


50.3242 


40.2072 


46 


1-2579 


7950 


51-5758 


41.0022 


47 


I .2642 


7910 


52.8337 


41-7932 


48 


1.2705 


7871 


54.0978 


42 - 5803 


49 


1.2768 


7832 


55-3683 


43-3635 


60 


1.2832 


7793 


56-6452 


44.1428 


65 


1-3156 


7601 


63 . 1 200 


47.9782 


60 


1.3488 


7414 


69.7600 


51.7020 


65 


1.3829 


7231 


76.5800 


55-2764 


70 


I. 4178 


7053 


83 . 5600 


58-9364 


75 


1-4536 


6879 


90.7200 


62.4745 


80 


1-4903 


6710 


98 . 0600 


65.7988 


85 


1.5280 


6545 


105.6000 


69 . 1099 


90 


1.5665 


6383 


113.3000 


72.3268 


96 


I. 6061 


6226 


121.2200 


75-4747 


100 


I . 6467 


6073 


129.3400 


78.5449 


105 


1.6882 


5923 


137.6400 


81.5306 


100 


1-7309 


5777 


146.1800 


84.4531 


115 


1.7746 


5635 


154.9200 


87.298s 


120 


I. 8194 


5496 


163.8800 


90.0736 



APPENDIX 



251 



PER CENT 



« years. 


1. 


II. 


III. 


IV. 


1 


I. 0100 


.9901 


I . 0000 


.9901 


2 


I .0201 


.9803 


2.0100 


1.9704 


3 


I 0303 


.9706 


3 0301 


2 .9410 


4 


I . 0406 


.9610 


4 . 0604 


3.9020 


6 


I. 05 10 


•951S 


5.1010 


4-8534 


6 


I. 0615 


.9420 


6.1520 


5-7955 


7 


I. 0721 


■9327 


7-2135 


6.7282 


8 


1.0829 


•9235 


8.2857 


7-6517 


9 


I 0937 


•9143 


9.3685 


8.5660 


10 


I . 1046 


•9053 


10.4622 


9-4713 


11 


I-IIS7 


.8963 


11.5668 


10.3676 


12 


I. 1268 


.8874 


12.6825 


11-2551 


13 


1.1381 


.8787 


13 - 8093 


12.1337 


14 


I 1495 


.8700 


14-9474 


130037 


15 


1.1610 


.8613 


16.0969 


13-8651 


16 


I. 1726 


.8528 


17.2579 


14.7179 


17 


I. 1843 


.8444 


18.4304 


15-5622 


18 


I. 1961 


.8360 


19.6147 


16.3983 


19 


I. 2081 


.8277 


20.8109 


17 . 2260 


20 


1.2202 


.8195 


22.0190 


18.0456 


21 


1.2324 


.8114 


23.2392 


18.8570 


22 


1.2447 


.8034 


24.4716 


19.6604 


23 


1.2572 


-7954 


25-7163 


20.4558 


24 


I . 2697 


.7876 


26.9735 


21.2434 


26 


1.2824 


.7798 


28.2432 


22.0232 


26 


1-2953 


.7720 


29.5256 


22.7952 


27 


1.3082 


.7644 


30.8209 


23-5596 


28 


1.3213 


-7568 


32.1291 


24-3164 


29 


1-3345 


•7493 


33-4504 


25.0658 


30 


1-3478 


.7419 


34-7849 


25-8077 


31 


I -3613 


•7346 


36-1327 


26.5423 


32 


1-3749 


•7273 


37-4941 


27.2696 


33 


1-3887 


.7201 


38.8690 


27.9897 


34 


1.4026 


•7130 


40-2577 


28.7027 


35 


I .4166 


•7059 


41.6603 


29.4086 


36 


1.4308 


.6989 


43.0769 


30-1075 


37 


I-4451 


.6920 


44.5076 


30 - 7995 


38 


1-4595 


.6852 


45-9527 


31.4847 


39 


1. 4741 


.6784 


47-4123 


32.1630 


40 


1.4889 


.6717 


48.8864 


32.8347 


41 


1.S038 


■ 6650 


50.3752 


33-4997 


42 


I-S188 


.6584 


51.8790 


34-1581 


43 


I 5340 


.6519 


53-3978 


34.8100 


44 


I ■ 5493 


■6454 


54-9318 


35-4554 


45 


1.5648 


.6391 


56.4811 


36-0945 


46 


I. 580s 


•6327 


58-0459 


36.7272 


47 


1-5963 


.6265 


59-6263 


37-3537 


48 


I .6122 


.6203 


61.2226 


37-9740 


49 


1.6283 


.6141 


62 . 8348 


38.5881 


50 


I . 6446 


.6080 


64.4632 


39-1961 


65 


1.7284 


.5786 


72.8400 


42.1430 


60 


I. 8166 


■5505 


81.6600 


44-9521 


66 


I - 9093 


.5238 


90 . 9300 


47-6247 


70 


2 . 0066 


.4983 


100 . 6600 


50.1644 


76 


2. 1090 


•4742 


110.9000 


52.5841 


80 


2.2166 


.4500 


121. 6600 


54-8858 


85 


2.3296 


.4292 


132.9600 


57-0742 


90 


2.4485 


.4084 


144.8500 


59-1750 


95 


2.5733 


.3886 


157-3300 


61.1394 


100 


2 . 7046 


• 3697 


170.4600 


63.0259 


105 


2.8425 


.3518 


184.2500 


64.8197 


110 


2.9875 


.3347 


198.7500 


66.5272 


116 


3.1399 


.3185 


213.9900 


68.1518 


120 


3-3001 


■3030 


230.0100 


69.6979 



252 



APPENDIX 



ih PER CENT 



n years. 


I. 


II. 


III. 


IV. 


1 


I. 0150 


.9852 


I . 0000 


.9852 


2 


1.0302 


.9707 


2.0150 


1^9559 


3 


I 0457 


•9563 


3-0452 


2.9122 


4 


I .0614 


•9422 


4.0909 


3^8544 


6 


I 0773 


.9283 


5-1523 


4.7826 


6 


I -0934 


•9145 


6.2290 


5. 6972 


7 


I. 1098 


.9010 


7-3230 


6.5982 


8 


1. 1 265 


.8877 


8.4328 


7^4859 


9 


I -1434 


.8746 


9^5593 


8.3605 


10 


I . 160S 


.8617 


10.9027 


9.2222 


11 


1.1770 


.8489 


11.8633 


10.0711 


12 


I 1959 


.8364 


13.0412 


10.9075 


13 


1-2130 


.8240 


14.2368 


11-7315 


14 


I. 2318 


.8118 


15-4504 


12.5434 


15 


1.2502 


.7999 


16.6821 


13^3432 


16 


I . 2690 


.7880 


17-9324 


14-1313 


17 


1.2880 


.7764 


19-2014 


14-9076 


18 


1-3073 


.7649 


20.4894 


15.6726 


19 


1.3270 


•7536 


21.7967 


16.4262 


20 


1.3469 


•7425 


23-1237 


17.1686 


21 


I. 3671 


•731S 


24-4705 


17.9001 


22 


1-3876 


.7207 


25-8376 


18.6208 


23 


1.4084 


.7100 


27.2251 


19-3309 


24 


1.429s 


-6995 


28.6335 


20 . 0304 


25 


1.4509 


.6892 


30.0630 


20.7196 


26 


1.4727 


.6790 


31-5140 


21.3986 


27 


1.4948 


.6690 


32-9867 


22.0676 


28 


1-5172 


■ 6591 


34-4815 


22.7267 


29 


I - 5400 


.6494 


35-9987 


23.3761 


30 


1-5631 


.6398 


37-5387 


24.0158 


31 


1.5865 


.6303 


39-1018 


24 . 6461 


32 


I -6103 


.6210 


40.6883 


25.2671 


33 


1-6345 


.6118 


42.2986 


25 . 8790 


34 


1.6590 


.6028 


43-9331 


26.4817 


35 


1.6839 


■5939 


45-5921 


27.0756 


36 


I . 7091 


.5851 


47-2760 


27.6607 


37 


1-7348 


• 5764 


48-9851 


28.2371 


38 


I . 7608 


■ 5679 


50.7199 


28.8051 


39 


1.7872 


• 5595 


52.4807 


29.3646 


40 


I. 8140 


• 5513 


54-2679 


29.9158 


41 


I. 8412 


■ 5431 


56.0819 


30.4590 


42 


1.8688 


• 5351 


57-9231 


30.9940 


43 


1.8969 


• 5272 


59.7920 


31.5212 


44 


1-9253 


•S194 


61.6889 


32.0406 


46 


1-9542 


• 5117 


63.6142 


32.5523 


46 


1-9835 


.5042 


6s ■ 5684 


33-0565 


47 


2.0133 


.4967 


67-5519 


33-5532 


48 


2.043s 


.4894 


69-5652 


34-0426 


49 


■ 2.0741 


.4821 


7 1 . 6087 


34-5247 


60 


2.1052 


• 4750 


73-6828 


34-9997 


65 


2.2679 


• 4409 


84-5296 


37.2715 


60 


2.4432 


• 4093 


96.2147 


39-3803 


65 


2.6320 


•3799 


108.8000 


41-3373 


70 


2-8355 


•3527 


122.3640 


43-1549 


75 


3-0546 


• 3274 


136.9670 


44.8409 


80 


3 . 2907 


• 3039 


152.7110 


46.4073 


85 


3-S450 


.2821 


169.6600 


47 - 8603 


90 


3-8189 


.2618 


187.9300 


49.2099 ■ 


95 


4.1141 


• 2431 


207 . 6000 


50.4618 


100 


4.4320 


.2256 


228.8030 


51.6247 


105 


4-7746 


.2094 


251.6330 


52.7036 


110 


S-1436 


.if)44 . 


276.2380 


53-7055 


115 


S-5411 


.1805 


302.7330 


54-6351 


120 


5 ■ 9693 


• 1675 


331-2880 


55-4985 







APPENDIX 




253 






2 PER CENT 




n years. 


I. 


11. 


III. 


IV. 


1 


I.0200 


.9804 


I. 0000 


.9804 


2 


1.0404 


.9612 


2.0200 


I. 9416 


3 


I. 061 2 


.9423 


3.0604 


2.8839 


4 


1.0824 


.9238 


4. 1216 


3.8077 


6 


1.1041 


.9056 


5 - 2040 


4-7135 


6 


I. 1262 


.8880 


6.3081 


5.6014 


7 


I. 1487 


.8706 


7-4343 


6.4720 


8 


1.1717 


.8535 


8.5830 


7-3255 


9 


I. 1951 


.8368 


9-7546 


8.1622 


10 


I. 2190 


.8203 


10.9497 


8.9826 


11 


1-2434 


.8043 


12.1687 


9.7868 


12 


1.2682 


.7885 


13-4121 


10.5753 


13 


I . 2936 


.7730 


14.6803 


11.3484 


14 


1.3195 


■7579 


15-9739 


12.1062 


16 


1-3459 


.7430 


17-2934 


12.8493 


16 


1.3728 


.7284 


18.6393 


13-5777 


17 


I . 4002 


.7142 


20.0121 


14.2919 


18 


1.4282 


.7002 


21.4123 


14.9920 


19 


1.4568 


.6S64 


22.8406 


15.678s 


20 


1.4859 


.6730 


24.2974 


16.3514 


21 


1-5157 


.6598 


25-7833 


17.0112 


22 


1.5460 


.6468 


27.2990 


17.6580 


23 


1-5769 


.6342 


28.8450 


18.2922 


24 


I . 6084 


.6217 


30.4219 


18.9139 


25 


I . 6406 


.6095 


32.0303 


19.5235 


26 


1-6734 


.5976 


33-6709 


20. 1210 


27 


I . 7069 


-5859 


35-3443 


20.7069 


28 


I. 7410 


-5744 


37-0512 


21.2813 


29 


1.7758 


• 5631 


38-7922 


21.8444 


30 


1.8114 


•5521 


40.5681 


22.3965 


31 


1.8476 


• 5412 


42.3794 


22.9377 


32 


1.8845 


.5306 


44.2270 


23.4683 


33 


1.9222 


.5202 


46. 1 1 16 


23.9886 


34 


I . 9607 


.5100 


48-0338 


24.4986 


35 


1.9999 


.5000 


49.9945 


24.9986 


36 


2.0399 


.4902 


51-9944 


25.4888 


37 


2 . 0807 


.4806 


54.0343 


25-9695 


38 


2.1223 


.4712 


56.1149 


26 . 4406 


39 


2.1647 


.4619 


58.2372 


26.9026 


40 


2 . 2080 


• 4529 


60 . 4020 


27.3555 


41 


2.2522 


.4440 


62.6100 


27-7995 


42 


2. 2972 


■4353 


64.8622 


28.2348 


43 


2.3432 


.4268 


67.1595 


28.6616 


44 


2.3901 


.4184 


69.5027 


29.0800 


45 


2.4379 


.4102 


71.8927 


29 . 4902 


46 


2.4866 


.4022 


74-3306 


29.8923 


47 


2.5363 


-3943 


76.8172 


30.2866 


48 


2.5871 


.3865 


79-3535 


30.6731 


49 


2.6388 


-3790 


81.9406 


31.0521 


60 


2.6gi6 


-3715 


84-5794 


31-4236 


55 


2.9717 


-3365 


98-5865 


33-1748 


60 


3.2810 


-3048 


114.0520 


34.7609 


65 


3.6225 


.2760 


131. 1250 


36.1973 


70 


3-9995 


.2500 


149-9780 


37.4986 


76 


4-4158 


.2265 


170.7900 


38.6763 


80 


4-8754 


.2051 


193.7720 


39-7445 


85 


5.3828 


.1858 


219.1400 


40 . 7 1 1 1 


90 


5-9431 


.1683 


247.1570 


41.5869 


95 


6.5617 


.1524 


278.0850 


42.3800 


100 


7.2446 


.1380 


312.2320 


43-0984 


105 


7.9987 


.1250 


349.9300 


43-7489 


110 


8.8312 


.1132 


391-5590 


44-3382 


116 


9.7503 


.1026 


437-5150 


44-8719 


120 


10.7652 


.0929 


488.2580 


45-3554 



254 



APPENDIX 



2i PER CENT 



n years. 


I. 


II. 


III. 


IV. 


1 


1.0250 


9756 


I . 0000 


-9756 


2 


I . 0506 


9Si8 


2.0250 


1-9274 


3 


1.0769 


9286 


3-0756 


2 . 8560 


4 


1 . 1038 


9060 


4-1525 


3.7620 


5 


1-1314 


8839 


5-2563 


4-6458 


6 


I -1597 


8623 


6-3877 


5-5081 


7 


I. 1887 


8413 


7-5474 


6.3494 


8 


1 . 2 1 84 


8207 


8.7361 


7.1701 


9 


I . 2489 


8007 


9-9545 


7 - 9709 


10 


I. 2801 


7812 


I I . 2034 


8.7521 


11 


1.3121 


7621 


12.4835 


9-5142 


12 


1-3449 


7436 


13-7956 


10.2578 


13 


1.378s 


7254 


15.1404 


10.9832 


14 


I. 4130 


7077 


16.5190 


1 I . 6909 


15 


1-4483 


6905 


17-9319 


12.3814 


16 


I -484s 


6736 


19.3802 


13-0550 


17 


1.5216 


6572 


20.8647 


13.7122 


18 


1-5597 


6412 


22.3863 


14-3534 


19 


1-5987 


6255 


23.9460 


14-9789 


20 


1.6386 


6103 


25-5447 


15-5892 


21 


1.6796 


S9S4 


27-1833 


16.184s 


22 


I .7216 


5809 


28.8629 


16.7654 


23 


I .7646 


5667 


30.5844 


17-3321 


24 


I . 8087 


5529 


32.3490 


17.8850 


26 


1-8539 


5394 


34-1578 


18.4244 


26 


I . 9003 


5262 


36.0117 


18.9506 


27 


1.9478 


S134 


37-9120 


19.4640 


28 


1.996s 


5009 


39-8598 


19.9649 


29 


2 . 0464 


4887 


41-8563 


20.4535 


30 


2.0976 


4767 


43.9027 


20.9303 


31 


2 . 1 500 


4651 


46.0003 


21.3954 


32 


2.2038 


4538 


48-1503 


21 .8492 


33 


2.2589 


4427 


50.3540 


22 . 2919 


34 


2.3153 


4319 


52.6129 


22.7238 


35 


2.3732 


4214 


54.9282 


23-1452 


36 


2-4325 


4111 


57-3014 


23-5563 


37 


2.4933 


401 1 


59-7339 


23-9573 


38 


2.5557 


3913 


62.2273 


24.3486 


39 


2.6196 


3817 


64.7830 


24-7303 


40 


2.6851 


3724 


67.4026 


25.1028 


41 


2.7522 


3633 


70.0876 


25.4661 


42 


2 .8210 


3545 


72.8398 


25.8206 


43 


2.891S 


3458 


75.6608 


26.1664 


44 


2.9638 


3374 


78.5523 


26.5038 


45 


3-0379 


3292 


81.5161 


26.8330 


46 


3-1139 


3211 


84-5540 


27.1542 


47 


3-1917 


3133 


87.6679 


27-4675 


48 


3-271S 


3057 


90.8596 


27.7732 


49 


3-3533 


2982 


94.1311 


28.0714 


60 


3-4371 


2909 


97-4843 


28.3623 


56 


3.8888 


•2571 


115-551 


29.7140 


60 


4-3998 


2273 


135-992 


30.9087 


66 


4-9780 


2009 


159.120 


31-963 


70 


S-6321 


1775 


185.284 


32.898 


76 


6.3722 


1569 


214.888 


33-645 


80 


7 . 2096 


.1387 


248.383 


34-452 


86 


8.1570 


.1226 


286.280 


35 096 


90 


9.2289 


.1084 


329-154 


35.666 


95 


10.4416 


0958 


377-664 


36.171 


100 


II. 8137 


.0846 


432-549 


36.614 


105 


13.3661 


0748 


494.644 


37.007 


110 


15.1226 


0661 


564.902 


37-355 


115 


17.1098 


0584 


644.392 


37.664 


120 


19-3581 


0517 


734-326 


37-934 



APPENDIX 



255 



PER CENT 



« years. 


I. 


II. 


III. 


IV. 


1 


1.0300 


9709 


I. 0000 


.9709 


2 


I . 0609 


9426 


2.0300 


I -913s 


3 


1.0927 


9151 


3.0909 


2.8286 


4 


I 1255 


8885 


4-1836 


3-7171 


5 


I -1593 


8626 


5 -3091 


4-5797 


6 


1.1941 


8375 


6.4684 


S-4172 


7 


I .2299 


8131 


7.6625 


6 . 2303 


8 


I . 2668 


7894 


8.8923 


7.0197 


9 


I . 3048 


7664 


10.1591 


7.7861 


10 


1-3439 


7441 


11.4639 


8.5302 


11 


1.3842 


7224 


12.8075 


9.2526 


12 


1.4258 


7014 


14. 1920 


9 -9540 


13 


1.4685 


6810 


15-6178 


10.6350 


14 


I .5126 


661 1 


17.0863 


I I. 2961 


16 


1-5580 


6419 


18.5989 


11-9379 


16 


1.6047 


6232 


20.1569 


12.5611 


17 


1.6528 


6050 


21.7616 


13.1661 


18 


1.7024 


5874 


23.4144 


13-7535 


19 


1-7535 


5703 


25.1169 


14-3238 


20 


I . 8061 


5537 


26.8704 


14-8775 


21 


1.8603 


5375 


28.6765 


15-4150 


22 


I .9161 


5219 


30.5368 


15-9369 


23 


1-9736 


5067 


32-4529 


16.4436 


24 


2.0328 


4919 


34-4265 


16.9325 


25 


2.0938 


4776 


36-4593 


17-4131 


26 


2.1566 


4637 


38.5530 


17.8768 


27 


2.2213 


4502 


40 . 7096 


18.3270 


28 


2.2879 


4371 


42.9309 


18.7641 


29 


2.3566 


4243 


45.2189 


19.1885 


30 


2.4273 


4120 


47-5754 


19.6004 


31 


2.5001 


4000 


50.0027 


20 . 0004 


32 


2.5751 


3883 


52.5028 


20.3888 


33 


2.6523 


3770 


55-0778 


20.7658 


34 


2.7319 


3660 


57-7302 


21.1318 


36 


2.8139 


3554 


60.4621 


21 .4872 


36 


2.8983 


3450 


63.2759 


21.8323 


37 


2.9852 


33SO 


66.1742 


22.1672 


38 


3-0748 


3252 


69.1594 


22.4925 


39 


3-1670 


3158 


72.2342 


22.8082 


40 


3.2620 


3066 


75-4013 


23.1148 


41 


3-3599 


2976 


78.6633 


23.4124 


42 


3-4607 


2890 


82.0232 


23.7014 


43 


3-5645 


2805 


85-4839 


23.9819 


44 


3-6715 


2724 


89 . 0484 


24 -2543 


46 


3-7816 


2644 


92.7199 


24.5187 


46 


3-8950 


2567 


96.5015 


24-7754 


47 


4.0119 


2493 


100.3965 


25.0247 


48 


4-1323 


2420 


104.4084 


25.2667 


49 


4-2562 


2350 


108.5406 


25-5017 


50 


4-3839 


2281 


112.7969 


25.7298 


56 


5.0821 


1968 


136.072 


26.7744 


60 


5.8916 


1697 


163-053 


27-6756 


66 


6 . 8300 


1464 


194-333 


28.452 


70 


7.9178 


1263 


230.594 


29-123 


76 


9.1789 


1089 


272.630 


29.702 


80 


10.6409 


0940 


321.363 


30.201 


85 


12.3357 


.0811 


377-857 


30.701 


90 


14-3005 


.0699 


443-349 


31.002 


96 


16.5782 


.0603 


519-273 


31-323 


100 


19.2186 


.0520 


607 . 288 


31-599 


106 


22.2797 


.0449 


709-323 


31-838 


110 


25.8282 


.0387 


827.608 


32-043 


116 


29.9420 


.0334 


964.733 


32.220 


120 


34-7110 


.0288 


1123.70 


32.373 



256 



APPENDIX 



3^ PER CENT 



n years. 


1. 


1 


1-0350 


2 


I. 0712 


3 


I . 1087 


4 


I -1475 


6 


I. 1877 


6 


1.2293 


7 


1.2723 


8 


I. 3168 


9 


1.3629 


10 


I. 4106 


11 


I . 4600 


12 


1.5111 


13 


I . 5640 


14 


I. 6187 


15 


1-6753 


16 


I • 7340 


17 


1-7947 


18 


1-8575 


19 


1.922s 


20 


1.9898 


21 


2-0594 


22 


2-1315 


23 


2.2061 


24 


2.2833 


25 


2.3632 


26 


2.4460 


27 


2.5316 


28 


2.6202 


29 


2.7119 


30 


2.8068 


31 


2 . 9050 


32 


3 • 0067 


33 


3.1119 


34 


3.2209 


36 


3 3336 


36 


3-4503 


37 


3-57IO 


38 


3 . 6960 


39 


3-8254 


40 


3-9593 


41 


4.0978 


42 


4-2413 


43 


4-3897 


44 


4-5433 


46 


4.7024 


46 


4.8669 


47 


5-0373 


48 


5-2136 


49 


5-3961 


50 


5-5849 


66 


6.6331 


60 


7.8781 


65 


9-3567 


70 


1 1. 1 1 28 


75 


13.1986 


80 


15-6757 


85 


18.6179 


90 


22.1122 


95 


26.2623 


100 


31.1914 


105 


37-0456 


110 


43 - 9986 


115 


52-2565 


120 


62.0643 



II. 



.9662 

.9335 
.9019 

.8714 

.8420 

-8135 
.7860 

-7594 
-7337 
-7089 

.6849 
.6618 
-6394 
.6178 
-5969 
-5767 

• 5572 
-5384 
.5202 
.5026 

-4856 
.4692 
-4533 
.4380 
-4231 
,4088 
-3950 
-3817 
-3687 
-3563 
-3442 
-3326 
-3213 

• 3105 
-3000 
.2898 
.2800 
.2706 
.2614 
.2526 

-2440 
.2358 
.2278 
. 2201 
.2127 
-2055 
-1985 
.1918 
.1853 
.1791 
-1508 
. 1269 
. 1069 
.0900 
-0758 
-0638 

-0537 
.0452 
.0381 
.0321 
.0270 
.0227 
.0191 
.0161 



III. 



IV. 



I .0000 
2-0350 
3 . 1062 
4.2149 
5-3625 
6.5502 
7-7794 
9-0517 
10.3685 

11-7314 
13.1420 
14.6020 
16. 1130 
17 .6770 
19.2957 
20.9710 
22 .7050 
24.4997 
26.3572 
28.2797 
30.2695 
32.3289 
34.4604 
36.666s 
38.9499 
41-3131 
43-7591 
46.2906 
48.9108 
51.6227 

54-4295 
57-3345 
60.3412 
63-4532 
66.6740 
70.0076 
73-4579 
77.0289 
80.7249 
84-5503 
88.5095 
92.6074 
96.8487 
101.2383 
105.7817 
110.4840 
115-3510 
120,3883 
125 .6018 
130.9979 
160.947 
196.517 
238.763 
288,938 
348-531 
419-307 
503-368 
603 . 205 
721 .780 
862.612 
1029.874 
1228.53 
1464.471 
1744.69 



.9662 
I . 8997 
2.8016 
3-6731 
4-5151 
S-3286 
6-1145 
6.8740 
7.6077 
8.3166 
9.0016 
9.6633 
10.3027 
10.9205 
11-5174 
12 .0941 
12.6513 
13-1897 
13-7098 
14.2124 
14 . 6980 
15-1671 
15.6204 
16.0574 
16.4815 
16.8904 
17.2854 
17.6670 
18.0358 
18.3920 

18.7363 
19.0689 
19.3902 
19.7007 
20 . 0007 
20. 2905 
20.5705 
20.8411 
21 . 1025 
21.3551 
21-5991 
21.8349 
22.0627 
22.2828 
22.4955 
22 .7009 
22.8994 
23.0912 
23 .2766 
23-4556 
24.2641 
24.9447 
25.5168 
26.0004 
26.4067 
26.7488 
27 .0368 
27.2793 
27-4798 
27-6554 
27.8002 
27 .9221 
28.0247 
28.1111 







APPENDIX 




257 






4 PER CENT 




« years. 


I. 


II. 


III. 


IV. 


1 


I . 0400 


.9615 


I . 0000 


-961S 


2 


I. 0861 


.9246 


2 . 0400 


1.8861 


3 


I. 1249 


.8890 


3.1216 


2.7751 


4 


I . 1699 


.8548 


4.2465 


3-6299 


6 


1.2167 


.8219 


5 -4163 


4.4518 


6 


1.2653 


-7903 


6 . 6330 


5.2421 


7 


1-3159 


-7599 


7-8983 


6.0021 


8 


1.3686 


-7307 


9-2142 


6.7327 


9 


1.4233 


.7026 


10.5828 


7-4353 


10 


I . 4802 


.6756 


12.0061 


8.1109 


11 


1-5395 


.6496 


13.4864 


8.760s 


12 


I .6010 


.6246 


15 0258 


9-3851 


13 


1.6651 


.6006 


16.6268 


9.9856 


14 


1-7315 


-5775 


18.2919 


10.5631 


15 


I . 8009 


-5553 


20.0236 


11 . 1184 


16 


1-8730 


-5339 


21.8245 


11.6523 


17 


1-9479 


-5134 


23.6975 


12.1657 


18 


2.0258 


-4936 


25-6454 


12.6593 


19 


2.106S 


-4746 


27.6712 


13-1339 


20 


2.1911 


-4564 


29.7781 


13 • 5903 


21 


2.2788 


-4388 


31-9692 


14.0292 


22 


2.3699 


.4220 


34-2480 


14.4511 


23 


2.4647 


■4057 


36.6179 


14.8568 


24 


2.5633 


■3901 


39.0826 


15.2470 


26 


2.6658 


-3751 


41-6459 


15.6221 


26 


2.7725 


-3607 


44-3117 


15.9828 


27 


2.8834 


.3468 


47.0842 


16.3296 


28 


2.9987 


•3335 


49.9676 


16.6631 


29 


3-I187 


.3207 


52.9663 


16.9837 


30 


3-2434 


.3083 


56 . 0849 


17.2920 


31 


3-3731 


-2965 


59-3283 


17-5885 


32 


3-5081 


.2851 


62.7015 


17-8736 


33 


3.6484 


.2741 


66 . 2095 


18.1476 


34 


3-7943 


.2636 


69.8579 


18.4112 


35 


3-9461 


-2534 


73-6522 


18.6646 


36 


4-1039 


-2437 


77-5983 


18.9083 


37 


4.2681 


■ 2343 


81 .7022 


19. 1426 


38 


4-4388 


.2253 


85 - 7903 


19.3679 


39 


4.6164 


.2166 


90.4091 


19-5845 


40 


4.8010 


-2083 


95-0255 


19.7928 


41 


4-9931 


. 2003 


99.8265 


19-9931 


42 


5.1928 


. 1926 


104 . 8200 


20.1856 


43 


5-4005 


.1852 


110.0124 


20.3708 


44 


5-6165 


.1780 


115.4129 


20.5488 


45 


5.8412 


.1712 


121.0294 


20.7200 


46 


6.0748 


.1646 


126.8706 


20.8847 


47 


6.3178 


.1583 


132.9454 


21 .0429 


48 


6.5705 


.1522 


139.2632 


21.1951 


49 


6.8333 


■1463 


145-8337 


21.3415 


50 


7.1067 


.1407 


152.6671 


21.4822 


66 


8.6464 


-I157 


191. 159 


22.1086 


60 


10.5196 


-0951 


237.991 


22.6235 


66 


12.7987 


.0781 


294.967 


23.0466 


70 


15-5716 


.0642 


364.290 


23-3945 


75 


18.9453 


.0528 


448.642 


23.6281 


80 


23 . 0498 


•0434 


551-245 


23-9154 


85 


28.0436 


•0357 


676.090 


24.1085 


90 


34-1193 


.0293 


827.983 


24.2673 


95 


41-5114 


.0241 


1012.785 


24-3977 


100 


50-5049 


.0198 


1237.622 


24.5050 


105 


61 .4470 


.0163 


1511-175 


24.5931 


110 


74-7597 


.0134 


1843-992 


24.6656 


115 


90.9566 


.0110 


2248.915 


24-7251 


120 


110.663 


.0090 


2741-558 


1 24-7741 



258 



APPENDIX 



4| PER CENT 



« years. 


I. ] 


I. 


III. 


IV. 


1 


1.0450 


9569 


I. 0000 


.9569 


2 


I .0920 


9157 


2.0450 


1.8727 


3 


1.1412 


876s 


3.1370 


2 . 7490 


4 


1.192s 


8386 


4.2782 


3-5875 


6 


1.2462 


8022 


5.4707 


4-3900 


6 


1.3023 


7679 


6.7169 


5.1579 


7 


1.3609 


7348 


8.0192 


5 8927 


8 


I. 4221 


7032 


9.3800 


6.5959 


9 


I. 4861 


6729 


10.8021 


7 . 2688 


10 


1.5530 


6439 


12.2882 


7-9125 


11 


1.6229 


6162 


13.8412 


8.5289 


12 


I . 6959 


4897 


15.4640 


9.1186 


13 


1.7722 


5643 


17-1599 


9.6829 


14 


1.8519 


5400 


18.9321 


10. 2229 


15 


1-9353 


S167 


20.7841 


10.7395 


16 


2.0224 


4945 


22.7193 


11.2340 


17 


2.1134 


4732 


24.7417 


11.7072 


18 


2 . 2085 


4528 


26.8551 


12.1600 


19 


2.3079 


4333 


29.0634 


12.5933 


20 


2.4117 


4146 


31-3716 


13.0079 


21 


2.5202 


3968 


33-7831 


13.4047 


22 


2.6337 


3797 


36-3034 


13.7844 


23 


2.7522 


3634 


38.9370 


14.1478 


24 


2.8760 


3477 


41.6892 


14.4955 


26 


3.0054 


3327 


44-5652 


14.8282 


26 


3 . 1407 


3184 


47.5706 


15.1466 


27 


3.2820 


3047 


50.7113 


15.4513 


28 


3.4279 


2916 


53-9933 


15.7429 


29 


3 . 5840 


2790 


57-4230 


i6.02ig 


30 


3.7453 


2670 


61.0071 


16.2889 


31 


3.9139 


2555 


64.7524 


16.5444 


32 


4 . 0900 


2445 


68.6662 


16.7889 


33 


4.2740 


2340 


72.7562 


17.0229 


34 


4 . 4664 


2239 


77.0303 


17.2468 


36 


4.6673 


2143 


81.4966 


17.4610 


36 


4.8774 


2050 


86.1640 


1 7 . 6660 


37 


5.0969 


1962 


91.0413 


17.8622 


38 


5.3262 


1878 


96.1382 


18.0500 


39 


5-5659 


1797 


101.4644 


18.2297 


40 


5 -8164 


1719 


107.0303 


18.4016 


41 


6.0781 


164s 


112.8467 


18.5661 


42 


6.3516 


1574 


118.9248 


18.723s 


43 


6.6374 


1507 


125.2764 


18.8742 


44 


6.9361 


1442 


131-9138 


19.0184 


46 


7.2482 


1380 


138.8500 


19.1563 


46 


7-5744 


1320 


146.0982 


19.2884 


47 


7-9153 


1263 


153.6726 


19.4147 


48 


8.271S 


1209 


161.5879 


19.5356 


49 


8.6437 


1157 


169.8594 


19.6513 


60 


9.0326 


1 107 


178.5030 


19.7620 


55 


11.2563 


0888 


227.9180 


20.2480 


60 


14.0274 


0713 


289 . 4980 


20.6380 


66 


17.4807 


0572 


366.2380 


20.9509 


70 


21.7841 


0459 


461.8700 


21.2021 


75 


27.1470 


0368 


581.2670 


21.4118 


80 


33.8301 


0296 


729.5580 


21.5653 


85 


42.1585 


0237 


914-6330 


21.6951 


90 


52.5371 


0190 


1145.2700 


21.7992 


96 


65.4708 


OIS3 


1432.6840 


21.8828 


100 


81.5885 


0123 


1790.8600 


21.9499 


105 


101.674 


0098 


2237.2000 


22.0036 


110 


126.704 


0079 


2793.4300 


22.0468 


116 


157.897 


0063 


3486.6000 


22.0815 


120 


196.768 


0051 


4350.4000 


22.1093 



APPENDIX 



259 



S PER CENT 



n years. 


I. 


II. 


III. 


rv. 


1 


1.0500 


■ 9524 


I. 0000 


■9524 


2 


I. 1025 


.9070 


2.0500 


I 


8594 


3 


I. 1576 


.8638 


3-1525 


2 


7232 


4 


I-2ISS 


.8227 


4.3101 


3 


5460 


6 


1.2763 


.7835 


5-5256 


4 


3295 


6 


I. 3401 


.7462 


6.8019 


5 


0757 


7 


1-4071 


.7107 


8.1420 


5 


7864 


8 


1-4775 


.6768 


9-5491 


6 


4632 


9 


1-5513 


.6446 


11.0266 


7 


1078 


10 


1.6289 


.6139 


12.5779 


7 


7217 


11 


I. 7103 


-5847 


14 . 2068 


8 


3064 


12 


I.795Q 


.5568 


15-9171 


8 


8623 


13 


1.8856 


•5303 


17.7130 


9 


3936 


14 


1.9799 


•5051 


19.5986 


9 


8986 


15 


2.0789 


.4810 


21.5786 


10 


3797 


16 


2.1829 


.4581 


23-6575 


10 


8378 


17 


2.2920 


•4363 


25-8404 


II 


2741 


18 


2 . 4066 


•415s 


28.1324 


II 


6896 


19 


2.5270 


• 3957 


30.5390 


12 


0853 


80 


2.6533 


• 3769 


33 -0660 


12 


4622 


SI 


2.7860 


.3589 


35-7193 


12 


8212 


22 


2.9253 


.3418 


38-5052 


13 


1630 


23 


3-0715 


• 3256 


41-4305 


13 


4886 


24 


3-2251 


.3101 


44.5020 


13 


7986 


26 


3-3864 


.2953 


47.7271 


14 


0939 


26 


3-5557 


.2812 


51-1135 


14 


3752 


27 


3-7335 


.2678 


54.6691 


14 


6430 


28 


3-9201 


-2551 


58.4026 


14 


8981 


29 


4.1161 


.2429 


62.3227 


15 


1411 


30 


4-3219 


-2314 


66.4388 


15 


3725 


31 


4-5380 


.2204 


70.7608 


15 


5928 


32 


4.7649 


.2099 


75.2988 


15 


8027 


33 


5 0032 


.1999 


80.0638 


16 


0025 


34 


5 2533 


.1904 


85.0670 


16 


1929 


36 


5-5160 


.1813 


90.3203 


16 


3742 


36 


5-7918 


.1727 


95-8363 


16 


5469 


37 


6.0814 


.1644 


101.6281 


16 


7113 


38 


6.385s 


.1566 


107.7095 


16 


8679 


39 


6 . 7048 


.1491 


114.0950 


17 


0170 


40 


7.0400 


.1420 


120.7998 


17 


1591 


41 


7.3920 


-1353 


127.8398 


17 


2944 


42 


7.7616 


.1288 


135-2318 


17 


4232 


43 


8.1497 


.1227 


142.9933 


17 


5459 


44 


8.5572 


.1169 


151 -1430 


17 


6628 


46 


8.9850 


.1113 


139.7002 


17 


7741 


46 


9-4343 


.1060 


168.6852 


17 


8801 


47 


9 . 9060 


. 1009 


178.1194 


17 


9810 


48 


10.4013 


.0961 


188.0254 


18 


0772 


49 


10.9213 


.0916 


198.4267 


18 


1687 


50 


11.4674 


.0872 


209.3480 


18 


2559 


55 


14-6356 


.0683 


272.7130 


18 


633s 


60 


18.6792 


-0535 


353 5840 


18 


9293 


66 


23 - 8399 


.0419 


456.7980 


19 


1191 


70 


30.4264 


-0329 


588.5290 


19 


3427 


75 


38.8327 


-0257 


756.6540 


19 


4849 


80 


49.5614 


.0202 


971.2290 


19 


5965 


86 


63 - 2544 


-0158 


1245.0880 


19 


6838 


90 


80.7304 


.0124 


1594. 6100 


19 


7523 


96 


103-035 


.0097 


2040.7000 


19 


8058 


100 


131. 501 


.0076 


2610.0300 


19 


8479 


106 


167-833 


.0060 


3336.6600 


19 


8808 


110 


214.202 


-0047 


4264.0300 


19 


9066 


116 


273.382 


.0037 


5447-6400 


19 


9268 


120 


348.912 


.0029 


6958. 2400 


19 


9427 



26o 



APPENDIX 



Sl PER CENT 



n years. 


I. 


II. 


III. 


IV. 


1 


I -0550 


-9479 


I . 0000 


-9479 


2 


1. 1 130 


-8985 


2.0550 


1-8463 


3 


I. 1742 


.8516 


3.1680 


2.6979 


4 


I . 2388 


.8072 


4-3423 


3-5052 


6 


1.3070 


•7651 


5-5811 


4-2703 


6 


1.3788 


-7252 


6.8881 


4-9955 


7 


1-4547 


-6854 


8.2669 


5-6830 


8 


1-5347 


.6516 


9.7216 


6-3346 


9 


1 .6191 


.6176 


11.2563 


6.9522 


10 


I. 7081 


• 5854 


12.8754 


7-5376 


11 


I. 8021 


•5549 


14-5835 


8.0925 


12 


I. 9012 


.5260 


16.3856 


8.6185 


13 


2.0058 


.4986 


18.2868 


9.1171 


14 


2 . 1161 


.4726 


20.2926 


9-5896 


15 


2.232s 


■4479 


22.4087 


10.0376 


16 


2-3553 


.4246 


24.6411 


10.4622 


i" 


2.4848 


.4024 


26.9964 


10.8646 


18 


2.6215 


.3815 


29.4812 


II. 2461 


19 


2.7656 


.3616 


32.1027 


11.6077 


20 


2.9178 


-3427 


34-8683 


11.9504 


21 


3-0782 


-3249 


37-7861 


12.2752 


22 


3-2275 


• 3079 


40.8643 


12.5832 


23 


3.4262 


-2919 


44. I I 18 


12.8750 


24 


3.6146 


.2767 


47-5380 


13-1517 


25 


3-8134 


.2622 


51.1526 


13-4139 


26 


4-0231 


.2486 


54.9660 


13-6625 


27 


4.2444 


• 2356 


58.9891 


13.8981 


28 


4-4778 


-2233 


63-2335 


14. 1214 


29 


4.7241 


.2117 


67.7114 


14-3331 


30 


4 . 9840 


.2006 


71-4355 


14-5337 


31 


5-2581 


.1902 


774194 


14-7239 


32 


5-5473 


.1803 


82.6775 


14.9042 


33 


5-8524 


.1709 


88.2248 


15-0751 


34 


6.1742 


.1620 


94.0771 


15-2370 


35 


6.5138 


• 1535 


100.2514 


15-3906 


36 


6.8721 


-1455 


106.7652 


15-5361 


37 


7-2501 


-1379 


113-6373 


15.6740 


38 


7.6488 


-1307 


120.8873 


15.8047 


39 


8.0695 


.1239 


128.5361 


15.9287 


40 


8.5133 


•1175 • 


136.6056 


16.0461 


41 


8.9815 


.1113 


145 . I 189 


16.1575 


42 


9-4755 


-I05S 


154-1005 


16.2630 


43 


9.9967 


.1000 


163.5760 


16.3630 


44 


10.5465 


.0948 


173-5727 


16.4579 


46 


II. 1266 


.0899 


184.1192 


16.5477 


46 


11-7385 


.0852 


195-2457 


16.6329 


47 


12.3841 


.0807 


206.9842 


16.7137 


48 


13-0653 


.0765 


219.3684 


16.7902 


49 


13-7838 


.0725 


232.4336 


16.8628 


50 


14.5420 


.0688 


246.217s 


16.9315 


66 


19.0046 


.0526 


327-3563 


17.2251 


60 


24.8381 


■ 0403 


433-4200 


17.4498 


65 


32.4623 


.0308 


572.0364 


17.6216 


70 


43.4150 


.0230 


771.1818 


17-7630 


76 


56.7414 


.0176 


1,013.4800 


17.8614 


80 


72.4703 


.0138 


1,299.4600 


17.9309 


85 


94.7152 


.0106 


1,703.9127 


17.9898 


90 


123-7883 


.0081 


2,232.5145 


18.0349 


95 


161.7855 


.0062 


2,923.3727 


18.0694 


100 


211.4463 


.0047 


3,826.2963 


18.0958 


106 


276.3503 


.0036 


5,006.3691 


18.1160 


110 


361.2768 


.0028 


6,550.4873 


18.1315 


116 


472.0413 


.0021 


8,564-3873 


18.1433 


120 


616.9357 


.0016 


11,198.8309 


18.1523 







APPENDIX 




261 






6 PER CENT 




n years. 


I. 


II. 


III. 


IV. 


1 


1.0600 


-9434 


I . 0000 


.9434 


2 


1. 1236 


.8900 


2.0600 


I • 8334 


3 


1.1910 


.8396 


3-1836 


2.6730 


4 


1.2625 


.7921 


4-3746 


3.4651 ■ 


6 


1.3382 


.7473 


5-6371 


4.2124 


6 


1.418s 


.7050 


6-9753 


4-9173 


7 


I • 5036 


.6651 


8.3938 


5-5824 


8 


I • 5938 


.6274 


9 8975 


6.2098 


9 


1.689s 


.5919 


11-4913 


6.8017 


10 


1.7908 


.5584 


13.1808 


7-3601 


11 


1.8983 


.5268 


14.9716 


7 . 8869 


12 


2.0122 


.4970 


16.8699 


8.3838 


13 


2.1329 


.4688 


18.8821 


8.8527 


14 


2 . 2609 


.4423 


21.0151 


9.2950 


15 


2.3966 


.4173 


23.2760 


9.7122 


16 


2 . 5404 


.3936 


25-6725 


IO.IOS9 


17 


2.6928 


.3714 


28. 2129 


10.4772 


18 


2.8S43 


• 3503 


30.9057 


10.8276 


19 


30256 


.3305 


33 ■ 7600 


11.1581 


20 


3.2071 


.3118 


36.7856 


I I . 4699 


21 


3-3996 


.2942 


39-9927 


II. 7641 


22 


3.6035 


.2775 


43-3923 


12.0416 


23 


3.8197 


.2618 


46-9958 


12.3034 


24 


4.0489 


.2470 


50.8156 


12.5504 


25 


4.2919 


■ 2330 


54-8645 


12.7834 


26 


4-5494 


.2198 


59-1564 


13.0032 


27 


4.8223 


.2074 


63 - 7058 


13-2105 


28 


51117 


.1956 


68.5281 


13.4062 


29 


5-4184 


.1846 


73-6398 


13-5907 


30 


5-7435 


.1741 


79.0582 


13.7648 


31 


6.0881 


.1643 


84.8017 


13.9291 


32 


6-4534 


■1550 


go. 8898 


14.0840 


33 


6 . 8406 


.1462 


97.3432 


14.2302 


34 


7.2510 


.1379 


104.1838 


14.3681 


35 


7.6861 


.1301 


III. 4348 


14.4982 


36 


8.1473 


.1227 


119. 1209 


14.6210 


37 


8.6361 


.1158 


127.2681 


14-7368 


38 


9.1543 


.1092 


135.9042 


14.8460 


39 


9.703s 


.1031 


145-0585 


14.9491 


40 


10.2857 


.0972 


154.7620 


15-0463 


41 


10.9029 


.0917 


165.0477 


15.1380 


42 


11.5570 


-086s 


175-9505 


15-2245 


43 


12.2505 


.0816 


187.5076 


153062 


44 


12.985s 


.0770 


199.7580 


15-3832 


45 


13.7646 


.0727 


212.7435 


15-4558 


46 


14.5905 


-068s 


226.5081 


15-5244 


47 


15.4659 


-0647 


241.0985 


15-5890 


48 


16.3939 


.0610 


256.564s 


15.6500 


49 


17.3775 


-OS75 


272.9584 


15.7076 


50 


18.4202 


.0543 


290-3359 


15-7619 


55 


24.6507 


.0406 


394-1783 


15-9905 


60 


32.9883 


.0303 


533.1383 


16.1611 


65 


44.1458 


.0226 


719.0966 


16.2891 


70 


590772 


.0169 


967-9533 


16.3845 


76 


79 -0587 


.0126 


1,300.9783 


16.4558 


80 


105.7985 


.0095 


1,746.6416 


16.5091 


85 


141.5287 


.0071 


2,343-0450 


16.5489 


90 


189.4698 


• 0053 


3,141.1633 


16.5787 


95 


253-5538 


.0039 


4,209.2300 


16.6009 


100 


339-3125 


.0029 


5,638.5416 


16.6175 


105 


454.0770 


.0022 


7.SS1.2833 


16.6299 


110 


607.6591 


.0016 


10,110.9850 


16.6392 


115 


813.1867 


.0012 


13,536.4450 


16.6461 


120 


1088.2280 


.0009 


18,120.4667 


16.6513 



262 



APPENDIX 



7 PER CENT 



n years. 


I. 


II. 


III. 


IV. 


1 


I . 0700 


• 9346 


I . 0000 


.9328 


2 


I . i44g 


-8736 


2.0700 


I . 8043 


3 


1.2250 


-8163 


3.2142 


2.6228 


4 


I. 3108 


.7629 


4.4400 


3-3857 


5 


I .4026 


■ 7130 


5-7514 


4 . 0986 


6 


1.5007 


.6663 


7-3529 


4-7657 


7 


1.6058 


.6227 


8-6542 


5-3886 


8 


I. 7182 


.5820 


10.2600 


5.9700 


9 


1.838s 


•543g 


11.9786 


6-S143 


10 


I. 9671 


.5083 


13-8159 


7.0228 


11 


2 . 1049 


• 4751 


15-7843 


7-4971 


12 


2.2522 


-4440 


17.8886 


7-9414 


13 


2 . 4098 


•4150 


20.1400 


8.3557 


14 


2.578s 


.3878 


22.5500 


8.7442 


16 


2.7590 


.3624 


25.1286 


9.1071 


16 


2.9522 


-3387 


27.8886 


9-4457 


17 


3-1588 


.3161 


30.8400 


9.7686 


18 


3 3800 


-2959 


34 . 0000 


10.0571 


19 


3-6165 


.2765 


37-3786 


10.3343 


20 


3.8697 


.2584 


40.9528 


10.5928 


21 


4 . 1406 


• 2415 


44.8657 


10.8343 


22 


4.4304 


• 2257 


49.0057 


I I . 0600 


23 


4-7405 


.2109 


53-4343 


II. 2714 


24 


50724 


.1971 


55-3200 


11-4685 


25 


5-4275 


.1842 


63 - 2500 


11.6528 


26 


5-8075 


.1722 


68.6786 


11.8242 


27 


6.2140 


.1609 


74-4857 


11.9857 


28 


6 . 6490 


• 1504 


80 . 7000 


12.1357 


29 


7.1144 


.1406 


87.3346 


12.2757 


30 


7.6124 


• 1314 


94.4628 


12.4071 


31 


8.1452 


.1228 


102.0742 


12.5300 


32 


8.7154 


.1147 


no. 2700 


12.6457 


33 


9-3255 


.1072 


118.9500 


12.7528 


34 


9-9783 


.1002 


128.2618 


12.8528 


35 


10.6768 


-0937 


138.2400 


12.9457 


36 


II. 4241 


-087s 


148.9157 


13-0343 


37 


12.2239 


.0818 


160.3414 


13-I157 


38 


13-0795 


.0765 


172.5642 


13-1914 


39 


13-9950 


-0715 


185.6428 


13.2628 


40 


14.9747 


.066S 


199.6386 


13-3300 


41 


16.0230 


.0624 


214-6143 


13-3928 


42 


17.1446 


.0583 


230.6371 


13-4514 


43 


18.3448 


-0545 


247.7828 


13-5057 


44 


19.6290 


.0509 


266. 1428 


13-5571 


45 


21.0030 


.0476 


285.7571 


13-6043 


46 


22.4332 


-044s 


306.1886 


13-6485 


47 


24 . 0463 


.0416 


329.2328 


13 . 6900 


48 


25.7888 


-0387 


354-1257 


13-7314 


49 


27-5306 


-0363 


379.0086 


13-7657 


50 


29-4577 


-0339 


406.5386 


13 . 8000 


55 


41.3162 


.0242 


575-9458 


13-9385 


60 


57.9482 


-0173 


813-5458 


14-0371 


65 


81-2755 


-0123 


1,146.7928 


14-1085 


70 


113.9929 


.0088 


1,614. 1844 


14-1585 


75 


159-8823 


.0062 


2,141.1757 


14.1959 


80 


224.2440 


-004s 


2,269.7471 


14.2200 


85 


314-5138 


.0032 


3,160.6285 


14-2385 


90 


441.1230 


.0023 


4,478.7682 


14.2514 


95 


618.7000 


.0016 


6,287.4714 


14.2614 


100 


867.7600 


.0011 


8,824.2857 


14.2685 


106 


1217.0812 


.0008 


12,382.2855 


14.2728 


110 


1707.023s 


.0006 


17,372.5886 


14-2757 


115 


2394.1978 


.0004 


24,371.7642 


14-2785 


120 


3357-9923 


.0003 


34,188.5400 


14 . 2800 



APPENDIX 



263 



8 PER CENT 



« years. 


I. 


II. 


III. 


IV. 


1 


1.0800 


.9259 


I. 0000 


.9250 


2 


1 . 1664 


-8573 


2.0800 


1.7825 


3 


1.2597 


-7938 


3 • 2463 


2.5762 


4 


1.3605 


• 7350 


4.5062 


3.3112 


6 


1.4693 


.6806 


5.8366 


3-9912 


6 


1.5869 


.6302 


7-3362 


4.6212 


7 


1.7138 


.5840 


8.922s 


5-1987 


8 


1.8509 


■5403 


10.6363 


5 - 7450 


9 


1.9990 


.5002 


12.4875 


6.2462 


10 


2.1589 


.4632 


14.4862 


6.7087 


11 


2.3317 


.4289 


16.6463 


7-1375 


12 


2.5182 


.3971 


18.977s 


7-5350 


13 


2.7196 


.3676 


21.4950 


7-9037 


14 


2.9372 


-3405 


24.2150 


8.2425 


16 


3.1722 


-3152 


27.1525 


8.5587 


16 


3.4260 


■ 2919 


30.3250 


8.8513 


17 


3 7000 


.2703 


33-7500 


9.1200 


18 


3.9960 


.2502 


37-4500 


9.3712 


19 


4-3157 


.2317 


41.4463 


9-6025 


20 


4.6610 


•214s 


45-7625 


9-8175 


21 


5 0339 


.1987 


50-4237 


10.0150 


22 


5.4366 


.1839 


55-4575 


10.2000 


23 


5-8716 


-1703 


60.8950 


10.3700 


24 


6-3413 


.1577 


66.7663 


10.5275 


26 


6.8486 


.1460 


73.1075 


10.6737 


26 


7 3964 


• 1352 


79 . 9800 


10.8087 


27 


7.9882 


.1252 


87.3525 


10.9337 


28 


8.6272 


■ 1159 


95.3400 


11.0500 


29 


9.3174 


-1073 


103-9675 


II.I575 


30 


10.0629 


.0994 


113.2862 


II .2562 


31 


10.8678 


.0920 


123.3475 


11-3487 


32 


11-7371 


-0852 


134-2138 


11-4337 


33 


12.6763 


.0789 


145-9537 


11-5125 


34 


13.6904 


-0730 


158.6300 


11.5862 


36 


14-7853 


.0676 


172.3163 


11.6537 


36 


15.9684 


.0626 


187.1050 


II. 7162 


37 


17.2460 


.0580 


203.0750 


11-7737 


38 


18.6249 


-0537 


220.3113 


11.8275 


39 


20.1159 


■ 0497 


238.9488 


11-8775 


40 


21.7250 


.0460 


259.0625 


11.9237 


41 


23.4630 


.0426 


280.7875 


11.9662 


42 


25-3400 


• 0395 


304.2500 


1 2 . 0050 


43 


27.3672 


-036s 


329.5900 


12.0425 


44 


29-5567 


-0338 


356.9588 


12.0762 


46 


31-9213 


• 0313 


386.5163 


12.1075 


46 


34-4750 


.0290 


418.4375 


12. 1362 


47 


37.2330 


.0269 


452.9125 


12.1625 


48 


40.2117 


.0249 


490.1463 


12.1875 


49 


43-4207 


.0230 


530.2588 


12.2112 


60 


46.9029 


.0213 


573.7863 


12.2325 


66 


68.9160 


.0145 


848 . 9500 


12.317s 


60 


101.2605 


.0099 


1,253.2563 


12.3750 


66 


148.7849 


.0067 


1,847.3113 


12.4150 


70 


218.6150 


.0046 


2,720.1875 


12.4412 


76 


321.2177 


.0031 


4,002.7213 


1 2 . 4600 


80 


471.9761 


.0021 


5,887.2013 


12.4725 


86 


693.4888 


.0014 


8,656.1100 


12.4812 


90 


1,018.9649 


.0010 


12,724.5613 


12.4862 


96 


1,497.1993 


.0007 


18,702.4913 


12.4900 


100 


2,199.8838 


.0005 


27,486.0475 


12.4925 


106 


3,232.3656 


.0003 


40,392.0700 


12.4950 


110 


4,749.4130 


.0002 


59,355.1625 


12.4962 


lis 


6,978.4677 


.0001 


87,218.3463 


12.497s 


120 


10,253.6792 


.0001 


128,158.4900 


12.4989 



204 




APPENDIX 








10 PER CENT 




n years. 


I. 


II. 


III. 


IV. 


1 


I . lOOO 


.9091 


I . 0000 


0.908 


2 


I . 2IOO 


.8264 


2.1000 


1-735 


3 


I-33IO 


• 7513 


3.3100 


2.486 


4 


I. 4641 


.6830 


4 . 6410 


3.169 


6 


I. 6105 


.6209 


6. 1050 


3.790 


6 


1. 7716 


•5645 


7.7160 


4.354 


7 


1.9487 


.5132 


9.4870 


4.867 


8 


2.1436 


.4665 


I I . 4360 


5-334 


9 


2.3580 


.4241 


13 . 5800 


5 758 


10 


2.5938 


.3855 


15.9380 


6.144 


11 


2.8531 


.3505 


18.5310 


6.494 


12 


3.1385 


.3186 


21.3850 


6.813 


13 


3.4523 


.2897 


24-5230 


7.102 


14 


3.7976 


.2633 


27.9760 


7.366 


15 


4.1773 


.2394 


31.7730 


7.605 


16 


4.5950 


.2176 


35.9500 


7.823 


17 


5. 0545 


.1978 


40.5450 


8.021 


18 


5.5600 


.1799 


45 . 6000 


8.200 


19 


6. I 160 


.1635 


51.1600 


8.364 


20 


6.7276 


.i486 


57.2760 


8.513 


21 


7.4004 


• 1351 


64 . 0040 


8.648 


22 


8. 1404 


.1228 


71.4040 


8.771 


23 


8.9545 


.1117 


79.5450 


8.882 


24 


9 • 8500 


.1015 


88.5000 


8.984 


26 


10.8349 


.0923 


98.3490 


• 9 076 


26 


II. 9184 


.0839 


109.1840 


9.160 


27 


13. I 103 


.0763 


121. 1030 


9-236 


28 


14.4213 


.0693 


134.2130 


9.306 


29 


15.8634 


.0630 


148.6340 


9-369 


30 


17.4498 


.0573 


164.4980 


9.426 


31 


19.1948 


.0521 


181.9480 


9.478 


32 


21.1143 


.0474 


201.1430 


9-525 


33 


23.2257 


.0431 


222.2570 


9-568 


34 


25 . 5483 


.0391 


245.4830 


9.608 


35 


28.1032 


.0356 


271.0320 


9 643 


36 


30.9135 


.0324 


299.1350 


9-675 


37 


34.0049 


.0294 


330.0490 


9-705 


38 


37.4054 


.0273 


364.0540 


9-726 


39 


41.1460 


.0243 


401.4600 


9.756 


40 


45.2605 


.0221 


442.6050 


9-778 


41 


49.7866 


.0201 


487.8660 


9-798 


42 


54.7655 


.0183 


537.6550 


9.816 


43 


60. 2420 


.0166 


592.4200 


9 833 


44 


66.2662 


.0151 


652.6620 


9.848 


45 


72.8928 


.0137 


718.92S0 


9.862 


46 


80.1822 


.0125 


791.8220 


9-874 


47 


88.2004 


.0113 


872.0040 


9-886 


48 


97.0207 


• 0103 


960. 2070 


9.896 


49 


106.7228 


.0094 


1,057.2280 


9-905 


50 


117.3926 


.0085 


1,163.9260 


9-914 


55 


189.0668 


.0053 


1,880.6680 


9-946 


60 


304.4944 


• 0033 


3,034.9440 


9.966 


65 


490.3932 


.0020 


4,893.9320 


9-979 


70 


789.7876 


.0013 


7,887.8760 


9-986 


75 


1,271.9648 


.0008 


12,709.6480 


9.991 


80 


2,048.5188 


.0005 


20,475.1880 


9.994 


85 


3,299.1742 


.0003 


32,981.7420 


9.996 


90 


5.313.3659 


.0002 


53,123.6590 


9.997 


95 


8,557.2549 


.0001 


85,562.5490 


9.998 


100 


13,781.6139 


.00007 


137,806.1390 


9.9992 


105 


22,195.5102 


. 00005 


221,945.1020 


9.9994 


110 


35,746.1983 


. 00003 


357,451.9830 


9.9996 


115 


57,569.8666 


.00002 


575,688.6660 


9.9997 


120 


92,717.0213 


.00001 1 


927,160. 2130 


9.9998 



TABLB VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


lOO 


000000 


0434 


0868 


1301 


1734 


2166 


2598 


3029 


3461 


3891 


432 


lOI 


4321 


4751 


5181 


5609 


6038 


6466 


6894 


7321 


7748 


,^'74 


428 


102 


8600 


9026 


9451 


9876 


*03oo 


♦0724 


*ii47 


*i570 


*i993 


♦2415 


424 


103 


012837 


3259 


3680 


4100 


4521 


4940 


5360 


5779 


6197 


6616 


420 


104 


7033 


7451 


7868 


8284 


8700 


9116 


9532 


9947 


*036i 


*0775 416 1 


105 


021 1S9 


1603 


2016 


2428 


2841 


3252 


3664 


4075 


4486 


4896 


412 


106 


5306 


5715 


6125 


6533 


6942 


7350 


7757 


8164 


8571 


8978 


408 


107 


9384' 


9789 


*oi95 


*o6oo 


*ioo4 


*i4o8 


*l8l2 


*22l6 


♦2619 


*302I 


404 


108 


033424 


3826 


4227 


4628 


5029 


5430 


5830 


6230 


6629 


7028 


400 


109 


7426 


7825 


8223 


8620 


9017 


9414 


9811 


*0207 


*o6o2 


*0998 


397 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




434 


43 


87 


130 


174 


217 


260 


304 


347 


391 


434 




433 


43 


H 


130 


173 


217 


260 


303 


346 


390 


433 




432 


43 


86 


130 


173 


216 


259 


302 


346 


3^9 


432 




431 


43 


86 


129 


172 


216 


259 


302 


345 


388 


431 




430 


43 


86 


129 


172 


215 


258 


301 


344 


387 


430 




429 


43 


86 


129 


172 


215 


257 


300 


343 


386 


429 




428 


43 


86 


128 


171 


214 


257 


300 


342 


3^5 


428 




427 


43 


85 


128 


171 


214 


256 


299 


342 


384 


427 




426 


43 


85 


128 


170 


213 


256 


298 


341 


383 


426 




425 


43 


85 


128 


170 


213 


255 


298 


340 


383 


425 




424 


42 


85 


127 


170 


212 


254 


297 


339 


382 


424 




423 


42 


85 


127 


169 


212 


254 


296 


33? 


381 


423 


1 


422 


42 


84 


127 


169 


211 


253 


295 


338 


380 


422 




421 


42 


84 


126 


168 


211 


253 


295 


337 


379 


421 




420 


42 


84 


126 


168 


210 


252 


294 


336 


378 


420 


m 


419 


42 


84 


126 


168 


210 


251 


293 


335 


377 


419 


H 
< 


418 


42 


84 


125 


167 


209 


251 


293 


334 


376 


418 


417 


42 


83 


125 


167 


2^ 


250 


292 


334 


375 


417 


416 


42 


83 


125 


166 


250 


291 


333 


374 


416 




415 


42 


83 


125 


166 


208 


249 


291 


332 


374 


415 


J 


414 


41 


83 


124 


166 


207 


248 


290 


331 


373 


414 


< 


413 


41 


83 


124 


165 


207 


248 


289 


330 


372 


413 


z 


412 


41 


82 


124 


165 


206 


247 


288 


330 


371 


412 





411 


41 


82 


123 


164 


206 


247 


288 


329 


370 


411 


H 


410 


41 


82 


123 


164 


205 


246 


287 


328 


369 


410 


Oi 


409 


41 


82 


123 


164 


205 


245 


286 


327 


368 


409 





408 


41 


82 


122 


163 


204 


245 


286 


326 


367 


408 


O4 


(1, 


407 


41 


81 


122 


163 


204 


244 


285 


326 


366 


407 


406 


41 


81 


122 


162 


203 


244 


284 


325 


365 


406 


405 


41 


81 


122 


162 


203 


243 


284 


324 


365 


405 




404 


40 


8i 


121 


162 


202 


242 


2S3 


323 


364 


404 




403 


40 


81 


121 


161 


202 


242 


282 


322 


363 


403 




402 


40 


80 


121 


161 


201 


241 


281 


322 


362 


402 




401 


40 


80 


120 


160 


201 


241 


281 


321 


361 


401 




400 


40 


80 


120 


160 


200 


240 


280 


320 


360 


400 




399 


40 


80 


120 


160 


200 


239 


279 


319 


359 


399 




398 


40 


80 


119 


159 


199 


239 


279 


3'? 


358 


398 




397 


40 


79 


119 


159 


199 


238 


278 


318 


357 


397 




396 


40 


79 


119 


158 


198 


238 


277 


317 


356 


396 




395 


40 


79 


119 


158 


198 


237 


277 


316 


356 


395 




394 


39 


79 


118 


158 


197 


236 


276 


315 


355 


394 




393 


39 


79 


118 


157 


197 


236 


275 


314 


354 


393 




392 


39 


78 


118 


157 


196 


235 


274 


314 


353 


392 




391 


39 


78 


117 


156 


196 


235 


274 


313 


352 


391 




390 


39 


78 


117 


156 


195 


234 


273 


312 


351 


390 




389 


39 


78 


117 


156 


195 


233 


272 


311 


350 


389 




388 


39 


78 


116 


155 


194 


233 


272 


310 


349 


388 




Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



265 







TABI,E VII.— 


I.OGARITHMS OF NUMBERS. 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


no 


041393 


1787 


2182 


2576 


2969 


3362 


3755 


4148 


4540 


4932 


393 


in 


5323 


5714 


6105 


6495 


68S5 


7275 


7664 


8053 


8442 


8S30 


390 


113 


9218 


9606 


9993 


*038o 


*0766 


*ii53 


*i538 


*i924 


*2309 


*2694 


386 


"3 


053078 


3463 


3846 


4230 


4613 


4995 


5378 


5760 


6142 


6524 


383 


114 


/?°§ 


7286 


7666 


8046 


8426 


8805 


9185 


9563 


9942 


*032O 


379 


"5 


060698 


1075 


1452 


1829 


2206 


2582 


2958 


3333 


3709 


4083 


376 


116 


4458 


4832 


5206 


5580 


5953 


6326 


6699 


7071 


7443 


7815 


373 


"I 


8186 


8557 


8928 


9298 


9668 


*oo38 


*04o7 


*0776 


*ii45 


*i5i4 


370 


118 


071882 


2250 


2617 


2985 


3352 


3718 


4085 


4451 


4816 


5182 


366 


ng 


5547 


5912 


6276 


6640 


7004 


7368 


7731 


8094 


8457 


8819 


363 


120 


079181 


9543 


9904 


*0266 


*o626 


*0987 


*i347 


*i707 


*2o67 


*2426 


360 


121 


0S27S5 


3144 


3503 


3861 


4219 


4576 


4934 


5291 


5647 


6004 


357 


122 


6360 


6716 


7071 


7426 


7781 


8136 


8490 


8845 


9198 


9552 


355 


123 


9905 


♦0258 


*o6ii 


♦0963 


*I3I5 


*i667 


*20l8 


*2370 


*272I 


♦3071 


352 


124 


093422 


3772 


4122 


4471 


4S20 


5169 


5518 


5866 


6215 


6562 


349 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




^ll 


39 


77 


116 


155 


194 


232 


271 


310 


348 


3^2 




386 


39 


77 


116 


154 


193 


232 


270 


309 


347 


386 




385 


39 


77 


116 


154 


193 


231 


270 


308 


347 


3^5 




384 


3o 


77 


115 


154 


192 


230 


269 


307 


346 


384 




383 


38 


77 


"5 


153 


192 


230 


268 


306 


345 


383 




382 


3^ 


76 


"5 


153 


191 


229 


267 


306 


344 


382 




381 


38 


76 


114 


152 


191 


229 


267 


305 


343 


381 




380 


38 


76 


114 


152 


190 


228 


266 


304 


342 


380 




379 


38 


76 


114 


152 


190 


227 


265 


303 


341 


379 




378 


38 


76 


"3 


151 


189 


227 


265 


302 


340 


378 




377 


38 


75 


"3 


151 


189 


226 


264 


302 


339 


377 




376 


38 


75 


113 


150 


188 


226 


263 


301 


338 


376 




375 


38 


75 


113 


150 


188 


225 


263 


300 


33S 


375 


m 

H 

< 


374 


37 


75 


112 


150 


187 


224 


262 


299 


337 


374 


373 


37 


75 


112 


149 


187 


224 


261 


298 


336 


373 


372 


37 


74 


112 


149 


186 


223 


260 


298 


335 


372 


a. 


371 


37 


74 


III 


148 


186 


223 


260 


297 


334 


371 




370 


37 


74 


III 


148 


185 


222 


259 


296 


333 


370 


< 
z 




369 


37 


74 


III 


148 


185 


221 


258 


295 


332 


369 


368 


37 


74 


no 


147 


184 


221 


258 


294 


331 


368 


367 


37 


73 


no 


147 


184 


220 


257 


294 


330 


367 


366 


37 


73 


no 


146 


183 


220 


256 


293 


329 


366 


H 


365 


37 


73 


no 


146 


183 


219 


256 


292 


329 


365 


Oi 


364 


36 


73 


109 


146 


182 


218 


255 


291 


328 


364 




a. 



363 


36 


73 


109 


145 


182 


218 


254 


290 


327 


363 


362 


36 


72 


109 


145 


iSi 


217 


253 


290 


326 


362 


361 


36 


72 


108 


144 


181 


217 


233 


2S9 


325 


361 


a, 


360 


36 


72 


108 


144 


180 


216 


252 


288 


324 


360 




359 


36 


72 


108 


144 


180 


215 


251 


287 


323 


359 




358 


36 


72 


107 


143 


179 


215 


251 


286 


322 


358 




357 


36 


71 


107 


143 


179 


214 


250 


286 


321 


357 




356 


36 


71 


107 


142 


178 


214 


249 


285 


320 


356 




355 


36 


71 


107 


142 


178 


213 


249 


284 


320 


355 




354 


35 


71 


106 


142 


177 


212 


248 


283 


319 


354 




353 


35 


71 


106 


141 


177 


212 


247 


282 


318 


353 




352 


35 


70 


106 


141 


176 


211 


246 


282 


317 


352 




351 


35 


70 


105 


140 


176 


211 


246 


281 


316 


351 




350 


35 


70 


105 


140 


175 


210 


245 


280 


315 


350 




349 


35 


70 


105 


140 


175 


209 


244 


279 


314 


349 




348 


35 


70 


104 


139 


174 


209 


244 


278 


313 


348 




347 


35 


69 


104 


139 


174 


208 


243 


278 


312 


347 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



266 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 
"5 


1 



I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

346 


096910 


7257 


7604 


7951 


8298 


8644 


8990 


9335 


9681 


*0026 


126 


10037 1 


0715 


1059 


1403 


1747 


2091 


2434 


2777 


3119 


3462 


343 


127 


3804 


4146 


4487 


4828 


5169 


5510 


5851 


6191 


6531 


6S7I 


34 1 


128 


7210 


7549 


7888 


8227 


8565 


8903 


9241 


9579 


9916 


*0253 


338 


129 


I I 0590 


0926 


1263 


1599 


1934 


2270 


2605 


2940 


3275 


3609 


335 


130 


I 13943 


4277 


461 1 


4944 


5278 


561 1 


5943 


6276 


6608 


6940 


333 


131 


7271 


7603 


7934 


8265 


8595 


8926 


9256 


9586 


9915 


*0245 


330 


132 


120574 


0903 


1231 


1560 


1888 


2216 


2544 


2871 


3198 


3525 


32S 


133 


3852 


4178 


4504 


4830 


5156 


5481 


5806 


6131 


6456 


6781 


325 


134 


7105 


7429 


7753 


8076 


8399 


8722 


9045 


9368 


9690 


*0O12 


323 


135 


130334 


0655 


0977 


1298 


1619 


1939 


2260 


2580 


2900 


3219 


321 


136 


3539 


3858 


4177 


4496 


4814 


5133 


5451 


5769 


6086 


6403 


318 


137 


6721 


7037 


..7354 


7671 


7987 


8303 


8618 


8934 


9249 


9564 


316 


138 


9879 


*oi94 


♦0508 


*0822 


*ii36 


*i450 


*I763 


♦2076 


♦2389 


*2702 


314 


139 


143015 


3327 


3639 


3951 


4263 


4574 


4885 


5196 


5507 


5818 


311 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


347 


35 


69 


104 


139 


174 


208 


243 


278 


312 


347 




346 


35 


69 


104 


^38 


173 


208 


242 


277 


3" 


346 




345 


35 


69 


104 


138 


173 


207 


242 


276 


3" 


345 




344 


34 


69 


103 


138 


172 


206 


241 


275 


310 


344 




343 


34 


69 


103 


137 


172 


206 


240 


274 


309 


343 




343 


34 


68 


103 


137 


171 


205 


239 


274 


308 


342 




341 


34 


68 


102 


136 


171 


205 


239 


273 


307 


341 




340 


34 


68 


102 


136 


170 


204 


238 


272 


306 


340 




339 


34 


68 


102 


136 


170 


203 


237 


271 


305 


339 




338 


34 


68 


lOI 


135 


169 


203 


237 


270 


304 


338 




337 


34 


67 


lOI 


135 


169 


202 


236 


270 


303 


337 




336 


34 


67 


lOI 


134 


168 


202 


235 


269 


302 


336 


w 


335 


34 


67 


lOI 


134 


168 


201 


235 


268 


302 


335 


H 


334 


33 


67 


100 


134 


167 


200 


234 


267 


301 


334 


di 


333 


33 


^l 


100 


133 


167 


200 


233 


266 


300 


333 


< 


332 


33 


66 


100 


133 


166 


199 


232 


266 


299 


332 


Oi 


331 


33 


66 


99 


132 


166 


199 


232 


265 


298 


331 


< 


330 


33 


66 


99 


132 


165 


198 


231 


264 


297 


330 


329 


33 


66 


99 


132 


165 


197 


230 


263 


296 


329 


2 


328 


33 


66 


98 


131 


164 


197 


230 


262 


295 


328 





327 


33 


65 


98 


131 


164 


196 


229 


262 


294 


327 




326 


33 


65 


98 


130 


163 


196 


228 


261 


293 


326 


325 


33 


^5 


98 


130 


163 


195 


228 


260 


293 


325 





324 


32 


65 


97 


130 


162 


194 


227 


259 


292 


324 


0. 


323 


32 


65 


97 


129 


162 


194 


226 


258 


291 


323 





322 


32 


64 


97 


129 


161 


193 


225 


258 


290 


322 


Oi 


321 


32 


64 


96 


128 


161 


193 


225 


257 


289 


321 


0* 


320 


32 


64 


96 


128 


160 


192 


224 


256 


288 


320 




319 


32 


64 


96 


128 


160 


191 


223 


255 


287 


319 




318 


32 


64 


95 


127 


159 


191 


223 


254 


286 


318 




317 


32 


63 


95 


127 


159 


190 


222 


254 


285 


317 




316 


32 


^3 


95 


126 


158 




221 


253 


284 


316 




315 


32 


f3 


95 


126 


158 


189 


221 


252 


284 


315 




314 


31 


63 


94 


126 


157 


188 


220 


251 


283 


314 




313 


31 


f3 


94 


125 


157 


188 


219 


250 


282 


313 




312 


31 


62 


94 


125 


156 


187 


218 


250 


281 


312 




3" 


31 


62 


93 


124 


156 


187 


218 


249 


280 


3" 




310 


31 


62 


93 


124 


155 


186 


217 


248 


279 


310 




309 


31 


62 


93 


124 


155 


185 


216 


247 


278 


309 




308 


31 


62 


92 


123 


154 


185 


216 


246 


277 


308 




307 


31 


61 


92 


123 


154 


184 


215 


246 


276 


307 
Diff. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 



267 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


140 


146128 


6438 


6748 


7058 


7367 


7676 


7985 


8294 


8603 


891 1 


309 


141 


9219 


9527 


9835 


*0142 


*0449 


*0756 


*io63 


*i370 


*i676 


*i982 


307 


142 


1522S8 


2594 


2900 


3205 


3510 


3815 


4120 


4424 


4728 


5032 


305 


143 


5336 


5640 


5943 


6246 


6549 


6852 


7154 


7457 


^7759 


8061 


303 


144 


8362 


8664 


8965 


9266 


9567 


9868 


*oi68 


♦0469 


*o769 


*io68 


301 


145 


161368 


1667 


1967 


2266 


2564 


2863 


3161 


3460 


3758 


4055 


299 


146 


4353 


4650 


4947 


5244 


5541 


5S38 


6134 


6430 


6726 


7022 


297 


147 


7317 


7613 


7908 


8203 


8497 


8792 


9086 


93S0 


9674 


9968 


295 


148 


170262 


0555 


0848 


II4I 


1434 


1726 


2019 


2311 


2603 


2895 


293 


149 


3186 


3478 


3769 


4060 


4351 


4641 


4932 


5222 


5512 


5S02 


291 


150 


I 7609 I 


6381 


6670 


6959 


7248 


7536 


7825 


8113 


8401 


8689 


289 


151 


8977 


9264 


9552 


9839 


*OI26 


*04i3 


*o699 


♦0986 


♦1272 


*I558 


287 


152 


181844 


2129 


2415 


2700 


2985 


3270 


3555 


3839 


4123 


4407 


2S5 


153 


4691 


4975 


5259 


5542 


5S25 


6108 


6391 


6674 


6956 


7239 


283 


154 


7521 


7803 


8084 


8366 


8647 


8928 


9209 


9490 


9771 


*oo5i 


281 


155 


190332 


0612 


0S92 


1171 


I45I 


1730 


2010 


2289 


2567 


2846 


279 


156 


3125 


3403 


3681 


3959 


4237 


4514 


4792 


5069 


5346 


5623 


27S 


157 


5900 


6176 


6453 


6729 


7005 


7281 


7556 


7832 


8107 


8382 


276 


158 


8657 


8932 


9206 


9481 


9755 


*0029 


♦0303 


*o577 


*o85o 


*II24 


274 


159 


201397 


1670 


1943 


2216 


2488 


2761 


3033 


3305 


3577 


3848 


272 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




306 


31 


61 


92 


122 


153 


184 


214 


245 


275 


306 




305 


31 


61 


92 


122 


153 


183 


214 


244 


275 


305 




304 


30 


61 


91 


122 


152 


182 


213 


243 


274 


304 




303 


30 


61 


91 


121 


152 


182 


212 


242 


273 


303 




302 


30 


60 


91 


121 


151 


181 


211 


242 


272 


302 




301 


30 


60 


90 


120 


151 


181 


211 


241 


271 


301 




300 


30 


60 


90 


120 


150 


180 


210 


240 


270 


300 




299 


30 


60 


90 


120 


150 


179 


209 


239 


269 


299 




298 


30 


60 


Sg 


119 


149 


179 


209 


238 


268 


298 




297 


30 


59 


89 


119 


149 


178 


208 


238 


267 


297 




296 


30 


59 


89 


118 


148 


178 


207 


237 


266 


296 


en 

H 


295 


30 


59 


89 


118 


148 


177 


207 


236 


266 


295 


294 


29 


59 


88 


118 


147 


176 


206 


235 


265 


294 


293 


29 


59 


88 


117 


147 


176 


205 


234 


264 


293 


b 


292 


29 


58 


88 


117 


146 


175 


204 


234 


263 


292 


< 


291 


29 


58 


87 


116 


146 


175 


204 


233 


262 


291 


290 


29 


58 


87 


116 


145 


174 


203 


232 


261 


ago 


2 


289 


29 


58 


87 


116 


145 


173 


202 


231 


260 


^^i 





288 


29 


58 


86 


"5 


144 


173 


202 


230 


259 


288 


H 


287 


29 


57 


86 


115 


144 


172 


201 


230 


258 


il 


:>!> 


286 


29 


57 


86 


114 


143 


172 


200 


229 


257 


286 





285 


29 


57 


86 


114 


143 


171 


200 


228 


257 


285 


cu 


284 


28 


57 


85 


114 


142 


170 


199 


227 


256 


284 





283 


28 


57 


85 


113 


142 


170 


198 


226 


255 


283 


K 


282 


28 


56 


85 


113 


141 


169 


197 


226 


254 


282 


& 


281 


28 


56 


84 


112 


141 


169 


197 


225 


253 


281 




280 


28 


56 


84 


112 


140 


168 


196 


224 


252 


280 




279 


28 


56 


84 


112 


140 


167 


195 


223 


251 


279 




278 


28 


56 


83 


III 


139 


167 


195 


222 


250 


278 




277 


28 


55 


83 


III 


139 


166 


194 


222 


249 


277 




276 


28 


55 


83 


no 


138 


166 


193 


221 


248 


276 




275 


28 


55 


83 


no 


138 


165 


193 


220 


248 


275 




274 


27 


55 


82 


no 


137 


164 


192 


219 


247 


274 




273 


27 


55 


82 


109 


137 


164 


191 


218 


246 


273 




272 


27 


54 


82 


109 


136 


163 


190 


218 


245 


272 




271 


27 


54 


81 


108 


136 


163 


I go 


217 


244 


271 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



268 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


i6o 


204120 


4391 


4663 


4934 


5204 


5475 


5746 


6016 


6286 


6556 


271 


lei 


6826 


7096 


~?Pb 


7634 


7904 


8173 


8441 


8710 


8979 


9247 


269 


162 


9515 


9783 


*oo5i 


*o3i9 


*0586 


*oS53 


*II2I 


♦1388 


*i654 


*I92I 


267 


163 


212188 


2454 


2720 


2986 


3252 


3518 


3783 


4049 


4314 


4579 


266 


164 


4844 


5109 


5373 


5638 


5902 


6166 


6430 


6694 


6957 


7221 


264 


165 


217484 


7747 


8010 


8273 


8536 


8798 


9060 


9323 


9585 


9846 


262 


•i66 


220108 


0370 


0631 


0892 


1 153 


1414 


1675 


1936 


2196 


2456 


261 


167 


2716 


2976 


3236 


3496 


3755 


4015 


4274 


4533 


4792 


5051 


259 


168 


5309 


5568 


5S26 


6084 


6342 


6600 


6S58 


71 15 


7372 


7630 


258 


i6g 


7887 


8144 


8400 


8657 


8913 


9170 


9426 


9682 


9938 


*oi93 


256 


170 


230449 


0704 


0960 


1215 


1470 


■1724 


1979 


2234 


2488 


2742 


255 


171 


2996 


3250 


3504 


3757 


401 1 


4264 


4517 


4770 


5023 


5276 


253 


172 


5528 


5781 


6033 


6285 


6537 


6789 


7041 


7292 


7544 


7795 


252 


173 


8046 


8297 


8548 


8799 


9049 


9299 


9550 


9800 


*oo5o 


*03OO 


250 


174 


240549 


0799 


1048 


1297 


1546 


1795 


2044 


2293 


2541 


2790 


249 


175 


243038 


3286 


3534 


37S2 


4030 


4277 


4525 


4772 


5019 


5266 


248 


176 


5513 


5759 




6252 


6499 


6745 


6991 


7237 


7482 


7728 


246 


177 


7973 


8219 


8464 


8709 


8954 


9198 


9443 


9687 


9932 


*oi76 


245 


178 


250420 


0664 


0908 


1151 


1395 


1638 


1881 


2125 


2368 


2610 


243 


179 


2853 


3096 


3338 


3580 


3822 


4064 


4306 


4548 


4790 


5031 


242 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




272 


27 


54 


82 


109 


136 


163 


190 


218 


245 


272 




271 


27 


54 


81 


108 


136 


163 


190 


217 


244 


271 




270 


27 


54 


81 


108 


135 


162 


189 


216 


243 


270 




269 


27 


54 


81 


108 


135 


161 


188 


215 


242 


269 




268 


27 


54 


80 


107 


134 


161 


188 


214 


241 


268 




267 


27 


53 


80 


107 


134 


160 


187 


214 


240 


267 




266 


27 


53 


80 


106 


133 


160 


186 


213 


239 


266 




265 


27 


53 


80 


106 


133 


159 


186 


212 


239 


265 




264 


26 


53 


79 


106 


132 


158 


185 


211 


238 


264 


CO 


263 


26 


55 


79 


105 


132 


158 


184 


210 


237 


263 


H 


262 


26 


52 


79 


105 


131 


157 


183 


210 


236 


262 


0!, 


261 


26 


52 


78 


104 


131 


157 


183 


209 


235 


261 


< 
0. 


260 


26 


52 


78 


104 


130 


156 


182 


208 


234 


260 


259 


26 


52 


78 


104 


130 


155 


181 


207 


233 


259 


< 



258 


26 


52 


77 


103 


129 


155 


181 


206 


232 


258 


257 


26 


51 


77 


103 


129 


154 


180 


206 


231 


257 


256 


26 


51 


77 


102 


128 


154 


179 


205 


230 


256 


255 


26 


51 


77 


102 


128 


153 


179 


204 


230 


255 


H 


254 


25 


51 


76 


102 


127 


152 


178 


203 


229 


254 


Oi 


253 


25 


51 


76 


lOI 


127 


152 


177 


202 


228 


253 




a. 



252 


25 


50 


76 


lOI 


126 


151 


176 


202 


227 


252 


251 


25 


50 


75 


100 


126 


151 


176 


201 


226 


251 


a: 


250 


25 


50 


75 


100 


125 


150 


175 


200 


225 


250 


o< 


249 


25 


50 


75 


100 


125 


149 


174 


199 


224 


249 




248 


25 


50 


74 


99 


124 


149 


174 


198 


223 


248 




247 


25 


49 


74 


99 


124 


148 


173 


198 


222 


247 




246 


25 


49 


74 


98 


123 


148 


172 


197 


221 


246 




245 


25 


49 


74 


98 


123 


147 


172 


196 


221 


245 




244 


24 


49 


73 


98 


122 


146 


171 


195 


220 


244 




243 


24 


49 


73 


97 


122 


146 


170 


194 


219 


243 




242 


24 


48 


73 


97 


121 


145 


169 


194 


218 


242 




241 


24 


48 


72 


96 


121 


145 


169 


193 


217 


241 




240 


24 


48 


72 


96 


120 


144 


168 


192 


216 


240 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diif. 



269 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


i8o 


255273 


5514 


5755 


5996 


6237 


6477 


6718 


6958 


7198 


7439 


241 


i8i 


7679 


7918 


8158 


8398 


8637 


8877 


9116 


9355 


9594 


9833 


239 


182 


260071 


0310 


0548 


0787 


1025 


1263 


1501 


1739 


1976 


2214 


238 


^^3 


2451 


26S8 


2925 


3162 


3399 


3636 


3873 


4109 


4346 


4582 


237 


184 


4818 


5054 


5290 


5525 


5761 


5996 


6232 


6467 


6702 


6937 


235 


185 


267172 


7406 


7641 


7875 


8110 


8344 


8578 


8812 


9046 


9279 


234 


186 


9513 


9746 


9980 


*02I3 


*0446 


*o679 


♦0912 


*ii44 


*i377 


*i6o9 


233 


187 


271842 


2074 


2306 


2538 


2770 


3001 


3233 


3464 


3696 


3927 


232 


188 


4158 


43S9 


4620 


4850 


5081 


531 1 


5542 


5772 


6002 


6232 


230 


189 


6462 


6692 


6921 


7151 


7380 


7609 


7838 


8067 


8296 


8525 


229 


190 


278754 


8982 


921 1 


9439 


9667 


9895 


*OI23 


*035i 


*0578 


*o8o6 


228 


191 


281033 


I261 


1488 


1715 


1942 


2169 


2396 


2622 


2849 


3075 


227 


192 


3301 


3527 


3753 


3979 


4205 


4431 


4656 


48S2 


5107 


5332 


226 


193 


5557 


5782 


6007 


6232 


6456 


6681 


6905 


7130 


7354 


7578 


225 


194 


7S02 


8026 


8249 


8473 


8696 


8920 


9143 


9366 


9589 


9812 


223 


195 


290035 


0257 


0480 


0702 


0925 


1 147 


1369 


1591 


1S13 


2034 


222 


196 


2256 


2478 


2699 


2920 


3141 


3363 


3584 


3804 


4025 


4246 


221 


197 


4466 


46S7 


4907 


5127 


5347 


5567 


5787 


6007 


6226 


6446 


220 


198 


6665 


68S4 


7104 


7323 


7542 


7761 


7979 


8198 


8416 


S635 


219 


199 


8853 


9071 


9289 


9507 


9725 


9943 


*ol6i 


*0378 


*0595 


*o8i3 


218 


200 


301030 


1247 


1464 


168 1 


1898 


2114 


2331 


2547 


2764 


2980 


217 


201 


3196 


3412 


3628 


3844 


4059 


4275 


4491 


4706 


4921 


5136 


216 


202 


5351 


5566 


5781 


5996 


6211 


6425 


6639 


6854 


7068 


7282 


215 


203 


7496 


7710 


7924 


8137 


S351 


8564 


8778 


8991 


9204 


9417 


213 


204 


9630 


9843 


♦0056 


*0268 


♦0481 


*o693 


♦0906 


*iii8 


*i330 


♦1542 


212 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




239 


24 


48 


72 


96 


120 


143 


167 


191 


215 


239 




238 


24 


48 


71 


95 


119 


143 


167 


190 


214 


238 




237 


24 


47 


71 


95 


119 


142 


166 


190 


213 


237 




236 


24 


47 


71 


94 


118 


142 


165 


189 


212 


236 




235 


24 


47 


71 


94 


118 


141 


165 


188 


212 


235 




234 


23 


47 


70 


94 


117 


140 


164 


187 


211 


234 




233 


23 


47 


70 


93 


117 


140 


163 


186 


210 


233 


CO 


232 


23 


46 


70 


93 


116 


139 


162 


186 


209 


232 


H 
< 


231 


23 


46 


69 


92 


116 


139 


162 


185 


208 


231 


230 


23 


46 


69 


92 


"5 


138 


161 


184 


207 


230 


0. 


229 


23 


46 


69 


92 


"5 


137 


160 


183 


206 


229 


>i 


228 


23 


46 


68 


91 


114 


137 


160 


182 


205 


228 


< 


227 


23 


45 


68 


91 


114 


136 


159 


182 


204 


227 


z 


226 


23 


45 


68 


90 


"3 


136 


158 


181 


203 


226 





225 


23 


45 


68 


90 


"3 


135 


158 


180 


203 


225 




224 


22 


45 


67 


90 


112 


134 


157 


179 


202 


224 


223 


22 


45 


67 


89 


112 


134 


156 


178 


201 


223 





222 


22 


44 


^J 


89 


III 


133 


155 


178 


200 


222 


Oi 


221 


22 


44 


66 


88 


III 


133 


155 


177 


199 


221 




pLt 


220 


22 


44 


66 


88 


no 


132 


154 


176 


198 


220 


219 


22 


44 


66 


88 


no 


131 


153 


175 


197 


2ig 




218 


22 


44 


f5 


f7 


109 


131 


153 


174 


196 


218 




217 


22 


43 


65 


87 


109 


130 


152 


174 


195 


217 




216 


22 


43 


65 


86 


108 


130 


151 


173 


194 


216 




215 


22 


43 


f5 


86 


108 


129 


151 


172 


194 


215 




214 


21 


43 


64 


86 


107 


128 


150 


171 


193 


214 




213 


21 


43 


64 


85 


107 


128 


149 


170 


192 


213 




212 


21 


42 


64 


85 


106 


127 


148 


170 


191 


212 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



270 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 
205 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


31 1754 


1966 


2177 


2389 


2600 


2812 


3023 


3234 


3445 


3656 


211 


206 


3S67 


4078 


4289 


4499 


4710 


4920 


5130 


5340 


5551 


5760 


210 


207 


5970 


6180 


6390 


6599 


6809 


7018 


7227 


7436 


7646 


7854 


209 


208 


8063 


8272 


8481 


8689 


8898 


9106 


9314 


9522 


9730 


9938 


208 


209 


320146 


0354 


0562 


0769 


0977 


1 184 


139 1 


1598 


1805 


2012 


207 


210 


322219 


2426 


2633 


2839 


3046 


3252 


3458 


3665 


3871 


4077 


206 


211 


42S2 


44S8 


4694 


4899 


5305 


5310 


5516 


5721 


5926 


6131 


205 


212 


6336 


6541 


6745 


6950 


7155 


7359 


75^3 


7767 


7972 


8176 


204 


213 


8380 


85S3 


8787 


8991 


9194 


9398 


9601 


9805 


*ooo8 


*02II 


203 


214 


330414 


0617 


0S19 


1022 


1225 


1427 


1630 


1832 


2034 


2236 


202 


215 


332(38 


2640 


2842 


3044 


3246 


3447 


3649 


3850 


4051 


4253 


202 


216 


4454 


4655 


4856 


5057 


5257 


5458 


565S 


5859 


6059 


6260 


201 


217 


6460 


6660 


6860 


7060 


7260 


7459 


7659 


7S58 


8058 


8257 


200 


218 


8456 


8656 


8855 


9054 


9253 


9451 


9650 


9849 


*0O47 


*0246 


199 


2ig 


340444 


0642 


0841 


1039 


1237 


1435 


1632 


1830 


202S 


2225 


198 


220 


342423 


2620 


2817 


3014 


3212 


3409 


3606 


3802 


3999 


4196 


197 


221 


4392 


4589 


47S5 


4981 


5178 


5374 


5570 


5766 


5962 


6157 


196 


222 


6353 


6549 


6744 


6939 


7135 


7330 


7525 


7720 


79 J 5 


8110 


195 


223 


8305 


8500 


8694 


8889 


9083 


9278 


9472 


9666 


9860 


*oo54 


194 


224 


350248 


0442 


o6s6 


0S29 


1023 


1216 


1410 


1603 


1796 


1989 


193 


225 


352183 


2375 


256S 


2761 


2954 


3147 


3339 


3532 


3724 


3916 


193 


226 


4108 


4301 


4493 


4685 


4876 


S068 


5260 


5452 


5643 


5834 


192 


227 


6026 


6217 


640S 


6599 


6790 


6981 


7172 


7363 


7554 


7744 


191 


228 


7935 


8125 


8316 


8506 


8696 


8886 


9076 


.9^^^ 


9456 


9646 


190 


229 


9835 


*0025 


*02I5 


*0404 


*0593 


*0783 


*0972 


*ii6i 


*i350 


*i539 


189 


230 


361728 


I9I7 


2105 


2294 


2482 


2671 


2859 


3048 


3236 


3424 


188 


231 


3612 


3S00 


39S8 


4176 


4363 


4551 


4739 


4926 


5113 


5301 


188 


232 


5488 


5675 


5862 


6049 


6236 


6423 


6610 


6796 


6983 


7169 


187 


233 


7356 


7542 


7729 


7915 


Sioi 


8287 


8473 


8659 


8845 


9030 


186 


234 


9216 


9401 


9587 


9772 


9958 


*oi43 


*032S 


*05i3 


*o69S 


*o883 


185 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




212 


21 


42 


64 


85 


106 


127 


148 


170 


191 


212 




211 


21 


42 


63 


84 


106 


127 


148 


169 


190 


211 




210 


21 


42 


63 


84 


105 


126 


147 


168 


189 


210 




209 


21 


42 


63 


84 


105 


125 


146 


167 


188 


209 




20S 


21 


42 


62 


83 


104 


125 


146 


166 


187 


208 


CO 


207 


21 


41 


62 


83 


104 


124 


145 


166 


186 


207 


206 


21 


41 


62 


82 


103 


124 


144 


165 


185 


206 


< 


205 


21 


41 


62 


82 


103 


123 


144 


164 


185 


205 


di 


204 


20 


41 


61 


82 


102 


, 122 


143 


163 


184 


204 


< 



203 


20 


41 


61 


81 


102 


122 


142 


162 


183 


203 


202 


20 


40 


61 


81 


lOI 


121 


141 


162 


182 


202 


201 


20 


40 


60 


80 


101 


121 


141 


161 


181 


2GI 


200 


20 


40 


60 


80 


100 


120 


140 


160 


180 


200 


H 


1 99 


20 


40 


60 


80 


100 


119 


139 


159 


179 


igg 


W 


198 


20 


40 


59 


79 


99 


119 


139 


^5^ 


178 


198 





197 


20 


39 


59 


79 


99 


118 


138 


158 


177 


197 


a< 


ig6 


20 


39 


59 


78 


98 


118 


137 


157 


176 


196 





195 


20 


39 


59 


78 


98 


117 


137 


156 


176 


195 


194 


19 


39 


58 


78 


97 


116 


136 


155 


175 


194 


J93 


19 


39 


58 


77 


97 


116 


135 


154 


174 


193 




192 


19 


38 


58 


77 


96 


"5 


134 


154 


173 


192 




igi 


19 


38 


57 


76 


96 


115 


134 


153 


172 


191 1 




190 


19 


38 


57 


76 


95 


114 


133 


152 


171 


190 1 




189 


19 


38 


57 


76 


95 


113 


132 


151 


170 


^?i 




188 


19 


38 


56 


75 


94 


113 


132 


150 


169 


188 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



271 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


235 
236 
237 
238 
239 
240 
241 
242 
243 
244 
245 
246 
247 
248 
249 
250 

251 
252 

253 
254 
255 
256 
257 
258 
259 
260 
261 
262 
263 
264 


371068 

2912 

4748 
6577 
8398 

380211 
2017 

3815 

5606 

7390 

389166 

390935 
2697 
4452 
6199 

397940 
9674 

40I40I 

3I2I 
4834 

406540 
8240 

9933 

41 1620 

3300 

414973 
6641 
8301 
9956 

421604 


3096 
4932 
6759 
8580 

0392 

2197 
3995 
57S5 
7568 
9343 
1112 
2873 
4627 
6374 
8114 
9847 
1573 
3292 
5005 
6710 
8410 

*0I02 

1788 
3467 

5140 
6807 
8467 
*0I2I 
1768 


1437 
32S0 

5115 
6942 
8761 

0573 
2377 
4174 
5964 
7746 
9520 
12S8 
3048 
4802 
6548 

8287 
*0020 
1745 
3464 
5176 

6SSi 
8579 

*027I 

1956 
3635 

5307 
6973 
8633 

*0286 
1933 


1622 
3464 
5298 
7124 

8943 

0754 
2557 
4353 
6142 

7923 
9698 
1464 
3224 
4977 
6722 

8461 

*OI92 

1917 
3635 
5346 
7051 
8749 

*0440 
2124 
3803 

5474 
7139 
8798 
0451 
2097 


1806 
3647 
5481 
7306 
9124 

0934 
2737 
4533 
6321 
8101 
9875 
1641 
3400 
5152 
6896 

8634 

*0365 
2089 
3807 
5517 
7221 
8918 

*o6o9 
2293 
3970 

5641 
7306 
8964 
*o6i6 
2261 


1991 

3831 
5664 
7488 
9306 

1115 
2917 
4712 
6499 
8279 

*0O'^I 

1817 

3575 
5326 
7071 

8808 
*o538 
2261 
3978 
5688 
7391 
90S7 
*0777 
2461 

4137 
5808 
7472 
9129 

*07Si 
2426 


2175 
4015 

5846 
7670 
9487 

1296 
3097 
4891 
6677 
8456 

*022S 
1993 
3751 
5501 
7245 
89S1 

*07ii 
2433 
4149 
5858 
7561 
9257 

*0946 
2629 
4305 

5974 
7638 
9295 
*0945 
2590 


2360 
4198 
6029 
7852 
9668 

1476 
3277 
5070 
6856 
8634 

*0405 
2169 
3926 
5676 
7419 

9154 
*o883 
2605 
4320 
6029 
7731 
9426 
*in4 
2796 
4472 
6141 
7804 
9460 

*II10 

2754 


2544 
4382 
6212 
8034 
9S49 

1656 
3456 
5249 
7034 
881 1 
♦0582 

2345 
4101 
5850 
7592 
9328 
*io56 
2777 
4492 
6199 
7901 

9595 

*12S3 

2964 

4639 

6308 

7970 

^9^25 

*i275 

2918 


2728 
4565 
6394 
8216 
*oo30 

1837 
3636 
542S 
7212 
89S9 

*o759 
2521 

4277 
6025 
7766 

9501 

*I228 
2949 
4663 
6370 
8070 
9764 

*i45i 
3132 
4806 

6474 
8135 
9791 
*I439 
30S2 


1S4 
1 84 
183 
182 
181 

181 
180 
179 
178 
178 
177 
176 
176 
175 
174 

173 
173 
172 
171 
171 
170 
169 
160 
168 
167 

167 
166 
165 
165 
164 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


CO 

H 
< 

a* 
< 

2 



H 



0. 


V, 
0. 


187 
186 

184 

182 
181 
180 

179 
178 
177 
176 
175 
174 
173 
172 
171 
170 

169 
168 
167 
166 
165 
164 


19 
19 

19 
18 
18 
18 
18 
18 

18 
18 
18 
18 
18 
17 
17 
17 
17 
17 

17 
17 
17 
17 
17 
16 


37 

37 
37 
37 
37 

36 

36 
35 
35 
35 
35 
35 
34 
34 
34 

34 
34 
33 
33 
33 
33 


5^ 
56 

56 

55 
55 
55 
54 
54 

54 
53 
53 
53 
53 
52 
52 
52 
51 
51 

51 
50 
50 
50 
50 
49 


75 
74 
74 
74 
73 
73 
72 
72 

72 
71 
71 
70 
70 
70 

^9 
69 

68 

68 

68 

67 
66 
66 
66 


94 
93 
93 
92 
92 
91 
91 
90 

90 
89 
89 
88 
88 
87 
87 
86 
86 
85 

^5 
84 

^4 
^3 
83 

82 


112 
112 
III 
110 
no 
109 

109 
108 

107 
107 

106 

106 
105 

104 

104 

103 
103 

102 

101 
101 
100 
100 

99 
98 


131 
130 
130 
129 
128 
127 
127 
126 

125 
125 
124 
123 
123 
122 
121 
120 
120 
119 

118 
118 
117 
116 
116 
115 


150 
149 
148 

147 
146 
146 
145 
144 

143 
142 
142 
141 
140 
139 
138 
138 
137 
136 

135 
134 
134 
133 
132 
131 


168 
167 
167 
166 

165 
164 
163 
162 

161 
160 
159 
158 
158 
157 
156 
155 
154 
153 
152 
151 
150 
149 
149 
148 


187 
186 

184 
183 
182 
181 
180 

179 
178 
177 
176 
175 
174 
173 
172 
171 
170 

169 
168 
167 
166 

165 
164 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 







TABtE VII.— LOGARITHMS OF NUMBERS. 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

164 


265 


423246 


3410 


3574 


3737 


3901 


4065 


4228 


4392 


4555 


4718 


266 


48S2 


5045 


5208 


5371 


5534 


5697 


5860 


6023 


6x86 


6349 


163 


267 


6511 


6674 


6836 


6999 


716X 


7324 


7486 


764S 


7811 


7973 


162 


268 


8135 


S297 


8459 


8621 


8783 


8944 


9106 


9268 


9429 


9591 


162 


269 


9752 


9914 


*oo75 


♦0236 


*0398 


*0559 


*0720 


*o8Si 


*I042 


*I203 


l6i 


270 


431364 


1525 


1685 


1846 


2007 


2167 


2328 


2488 


2649 


2809 


161 


271 


2969 


3130 


3290 


3450 


3610 


3770 


3930 


4090 


4249 


4409 


160 


272 


4569 


4729 


4888 


5048 


5207 


5367 


5526 


5685 


5844 


6004 


159 


273 


6163 


6322 


6481 


6640 


6799 


6957 


7II6 


7275 


7433 


7592 


159 


274 


7751 


7909 


8067 


8226 


8384 


8542 


8701 


8S59 


9017 


9175 


158 


275 


439333 


9491 


9648 


9806 


9964 


*OI22 


*0279 


*0437 


*o594 


*o752 


158 


276 


440909 


1066 


1224 


1381 


1538 


1695 


1852 


2009 


2166 


2323 


157 


277 


2480 


2637 


2793 


2950 


3106 


3263 


3419 


3576 


3732 


3889 


157 


278 


4045 


4201 


4357 


4513 


4669 


4825 


4981 


5137 


5293 


5449 


156 


279 


5604 


5760 


5915 


6071 


6226 


6382 


6537 


6692 


6848 


7003 


155 


280 


447158 


7313 


7468 


7623 


7778 


7933 


80S8 


8242 


8397 


8552 


155 


281 


8706 


8861 


9015 


9170 


9324 


9478 


9633 


9787 


9941 


*0095 


154 


282 


450249 


0403 


0557 


07 1 1 


0865 


1018 


1172 


1326 


1479 


1633 


154 


283 


1786 


1940 


2093 


2247 


2400 


2553 


2706 


2859 


3012 


3165 


153 


284 


3318 


3471 


3624 


3777 


3930 


4082 


4235 


4387 


4540 


4692 


153 


285 


454845 


4997 


5150 


5302 


5454 


5606 


5758 


5910 


60b 2 


6214 


152 


286 


6366 


6518 


6670 


6821 


6973 


7125 


7276 


7428 


7579 


7731 


152 


287 


7882 


8033 


S184 


8336 


8487 


8638 


8789 


8940 


9091 


9242 


151 


288 


9392 


9543 


9694 


9S45 


9995 


*oi46 


♦0296 


*0447 


*o597 


*0748 


151 


289 


460898 


1048 


1 198 


1348 


1499 


1649 


1799 


1943 


2098 


2248 


150 


2go 


462398 


2548 


2697 


2847 


2997 


3146 


3296 


3445 


3594 


3744 


150 


2gi 


3S93 


4042 


4191 


4340 


4490 


4639 


4788 


4936 


5085 


5234 


149 


292 


5383 


5532 


5680 


5829 


5977 


6126 


6274 


6423 


6571 


6719 


149 


293 


6868 


7016 


7164 


7312 


7460 


760S 


7756 


7904 


8052 


8200 


148 


294 


8347 


8495 


8643 


8790 


8938 


9085 


9233 


9380 


9527 


9675 


148 


295 


469822 


9969 


*oii6 


*0263 


*04io 


*0557 


*0704 


*o85i 


*o9q8 


*ii45 


147 


296 


471292 


1438 


1585 


1732 


1878 


2025 


2171 


2318 


2464 


2610 


146 


297 


2756 


2903 


3049 


3195 


3341 


3487 


3633 


3779 


3925 


4071 


146 


298 


4216 


4362 


4508 


4653 


4799 


4944 


5090 


5235 


5381 


5526 


146 


299 


5671 


5816 


5962 


6107 


6252 


6397 


6542 


6687 


6832 


6976 


145 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 
164 




164 


16 


33 


49 


66 


82 


98 


"5 


131 


148 




163 


16 


33 


49 


65 


82 


98 


114 


130 


147 


163 




162 


16 


32 


49 


65 


81 


97 


"3 


130 


146 


162 




161 


16 


32 


48 


64 


81 


97 


"3 


129 


145 


161 


CO 

H 


160 


16 


32 


48 


64 


80 


96 


112 


128 


144 


160 


159 


16 


32 


48 


64 


80 


95 


III 


127 


143 


159 


< 


158 


16 


32 


47 


63 


79 


95 


III 


126 


142 


158 


04 


157 


16 


31 


47 


63 


79 


94 


no 


126 


141 


157 


J 


156 


16 


31 


47 


62 


78 


94 


109 


125 


140 


155 


<< 


155 


16 


31 


47 


62 


78 


93 


109 


124 


140 


155 


2 


154 


15 


31 


46 


62 


77 


92 


108 


123 


139 


154 





153 


15 


31 


46 


61 


77 


92 


107 


122 


138 


153 




152 


15 


30 


46 


61 


76 


91 


106 


122 


137 


152 


Oi 



151 


15 


30 


45 


60 


76 


91 


106 


121 


136 


151 


150 


15 


30 


45 


60 


75 


90 


105 


120 


135 


150 


0, 




149 


15 


30 


45 


60 


75 


89 


104 


119 


134 


149 


148 


15 


30 


44 


59 


74 


^2 


104 


118 


133 


148 


147 


15 


29 


44 


59 


74 


88 


103 


118 


132 


147 




146 


15 


29 


44 


58 


73 


88 


102 


117 


131 


146 




M5 


15 


29 


44 


58 


73 


^I 


102 


116 


131 


145 




144 


14 


29 


43 


58 


72 


86 


lOI 


115 


130 


144 




143 


14 


29 


43 


57 


72 


86 


100 


114 


129 


143 


Diff. 


I 


1 2 


1 3 


I ^ 


5 


6 


7 


8 


9 


Diff. 



273 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 
145 


300 


477121 


7266 


7411 


7555 


7700 


7844 


7989 


8133 


8278 


8422 


301 


8566 


8711 


8S55 


8999 


9143 


9287 


9431 


9575 


9719 


9863 


144 


302 


480007 


0151 


0294 


0438 


0582 


0725 


0S69 


1012 


1 156 


1299 


144 


303 


1443 


15S6 


1729 


1872 


2016 


2159 


2302 


2445 


2588 


2731 


143 


304 


2874 


3016 


3159 


3302 


3445 


3587 


3730 


3872 


4015 


4157 


143 


305 


484300 


4442 


45S5 


4727 


4869 


501 1 


5153 


5295 


5437 


5579 


142 


306 


5721 


5S63 


6005 


6147 


6289 


6430 


6572 


6714 


6855 


6997 


142 


307 


7138 


72S0 


7421 


7563 


7704 


7S45 


7986 


8127 


8269 


8410 


141 


308 


8551 


S692 


8833 


8974 


..91 14 


9255 


9396 


9537 


9677 


9818 


141 


309 


9958 


*0099 


*0239 


♦0380 


*0520 


*o66i 


*oSoi 


*094i 


*io8i 


*I222 


140 


310 


491362 


1502 


1642 


1782 


1922 


2062 


2201 


2341 


2481 


2621 


140 


3" 


2760 


2900 


3040 


3179 


3319 


3458 


3597 


3737 


3876 


4015 


139 


312 


4155 


4294 


4433 


4572 


47II 


4850 


4989 


5128 


5267 


5406 


139 


313 


5544 


56S3 


5822 


5960 


6099 


6238 


6376 


6515 


6653 


6791 


139 


3M 


6930 


7068 


7206 


7344 


7483 


7621 


7759 


7897 


8035 


8173 


138 


315 


4983 11 


8448 


8586 


8724 


8S62 


8999 


9137 


9275 


..9412 


9550 


138 


316 


96S7 


9824 


9962 


*oo99 


*0236 


*0374 


*05ii 


*o648 


*0785 


*og22 


137 


317 


501059 


1196 


1333 


1470 


1607 


1744 


18S0 


2017 


2154 


2291 


137 


318 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 


3518 


3655 


136 


319 


3791 


3927 


4063 


4199 


4335 


4471 


4607 


4743 


4878 


5014 


136 


320 


505150 


5286 


5421 


5557 


5693 


5828 


5964 


6099 


6234 


6370 


136 


321 


6505 


6640 


6776 


6911 


7046 


7181 


7316 


7451 


75S6 


7721 


135 


322 


7856 


7991 


8126 


8260 


8395 


8530 


S664 


8799 


8934 


9068 


135 


323 


9203 


9337 


9471 


9606 


9740 


9874 


*ooo9 


*oi43 


*0277 


*04II 


134 


324 


510545 


0679 


0813 


0947 


1081 


1215 


1349 


1482 


1616 


1750 


134 


325 


5 I 1883 


2017 


2151 


2284 


241S 


2551 


2684 


2818 


2951 


3084 


133 


326 


3218 


3351 


3484 


3617 


3750 


3883 


4016 


4149 


4282 


4415 


133 


327 


4548 


46S1 


4813 


4946 


5079 


5211 


5344 


5476 


5609 


5741 


133 


328 


5S74 


6006 


6139 


6271 


6403 


6535 


6668 


6800 


6932 


7064 


132 


329 


7196 


7328 


7460 


7592 


7724 


7855 


7987 


8119 


8251 


8382 


132 


330 


518514 


8646 


8777 


8909 


9040 


9171 


9303 


9434 


.9566 


9697 


131 


331 


9S28 


9959 


*oo90 


*022I 


*0353 


*o4S4 


*o6i5 


*0745 


*o876 


*ioo7 


131 


332 


521 138 


1269 


1400 


1530 


1661 


1792 


1922 


2053 


2183 


2314 


131 


333 


2444 


2575 


2705 


2S35 


2966 


3096 


3226 


3356 


3486 


3616 


130 


334 


3746 


3876 


4006 


4136 


4266 


4396 


4526 


4656 


^785 


4915 


130 


335 


525045 


5174 


5304 


5434 


5563 


5693 


5822 


5951 


6081 


6210 


129 


336 


6339 


6469 


6598 


6727 


6855 


6985 


7114 


7243 


7372 


7501 


129 


337 


7630 


7759 


7888 


8016 


8145 


8274 


8402 


8531 


8660 


S7S8 


129 


338 


8917 


9045 


9174 


9302 


9430 


9559 


9687 


9815 


9943 


*0072 


128 


339 


530200 


0328 


0456 


0584 


0712 


0840 


0968 


1096 


1223 


I35I 


128 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 

128 


Diff. 
142 




142 


14 


28 


43 


57 


71 


85 


99 


114 


(» 


141 


14 


28 


42 


56 


71 


85 


99 


113 


127 


141 




140 


14 


28 


42 


56 


70 


84 


98 


112 


126 


140 


139 


14 


28 


42 


56 


70 


83 


97 


III 


125 


139 


& 


138 


14 


28 


41 


55 


69 


83 


97 


no 


124 


138 


< 
Z 



137 


14 


27 


41 


55 


69 


82 


96 


no 


123 


137 


136 


14 


27 


41 


54 


68 


82 


95 


109 


122 


136 


135 


14 


27 


41 


54 


68 


8i 


95 


108 


122 


135 


134 


13 


27 


40 


54 


67 


80 


94 


107 


121 


134 


133 


13 


27 


40 


53 


67 


80 


93 


106 


120 


133 


H 


132 


13 


26 


40 


53 


66 


79 


92 


106 


119 


132 





J31 


13 


26 


39 


52 


66 


79 


92 


105 


118 


131 


130 


13 


26 


39 


52 


65 


78 


91 


104 


117 


130 





I2g 


13 


26 


39 


52 


65 


77 


90 


103 


116 


129 


m 


128 


13 


26 


38 


51 


64 


77 


90 


102 


115 


128 


a. 


127 


13 


25 


38 


51 


64 


76 


89 


102 


114 


127 
Diff. 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 



274 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


34° 


531479 


1607 


1734 


1862 


1990 


2117 


2245 


2372 


2500 


2627 


128 


341 


2754 


2882 


3009 


3136 


3264 


3391 


3518 


3645 


3772 


3899 


127 


342 


4026 


4153 


4280 


4407 


4534 


4661 


4787 


4914 


5041 


5167 


127 


343 


5294 


5421 


5547 


5674 


5800 


5927 


6053 


618^ 


6306 


6432 


126 


344 


6558 


66S5 


681 1 


6937 


7063 


7189 


7315 


7441 


7567 


7693 


126 


345 


537819 


7945 


8071 


8197 


8322 


8448 


8574 


8699 


8825 


8951 


126 


346 


9076 


9202 


9327 


9452 


9578 


9703 


9829 


99u4 


*0079 


*0204 


125 


347 


540329 


0455 


0580 


0705 


0S30 


0955 


1080 


1205 


1330 


1454 


125 


348 


1579 


1704 


1S29 


1953 


207S 


2203 


2327 


2452 


2576 


2701 


125 


349 


2S25 


2950 


3074 


3199 


3323 


3447 


3571 


3696 


3820 


3944 


124 


35° 


54406S 


4192 


4316 


4440 


4564 


4688 


4812 


4936 


5060 


5183 


124 


351 


5307 


5431 


5555 


5678 


5S02 


5925 


6049 


6172 


6296 


6419 


124 


352 


6543 


6666 


67S9 


6913 


7036 


7159 


7282 


7405 


7529 


7652 


123 


353 


7775 


7S98 


8021 


8144 


8267 


8389 


8512 


8635 


8758 


8881 


123 


354 


9003 


9126 


9249 


9371 


9494 


9616 


9739 


9861 


9984 


*oio6 


123 


355 


550228 


0351 


0473 


0595 


0717 


0840 


0962 


1084 


1206 


1328 


122 


356 


1450 


1572 


Ib94 


1SI6 


1938 


2060 


2181 


2303 


2425 


2547 


122 


357 


2668 


2790 


2911 


3033 


3155 


3276 


339S 


3519 


3640 


3762 


121 


358 


3883 


4004 


4126 


4247 


4368 


4489 


4610 


4731 


4S52 


4973 


121 


359 


5094 


5215 


5336 


5457 


5578 


5699 


5820 


5940 


6061 


6182 


121 


360 


556303 


6423 


6544 


6664 


6785 


6905 


702S 


7146 


7267 


7387 


120 


361 


7507 


7627 


7748 


7S68 


79S8 


8108 


8228 


8349 


8469 


8589 


120 


362 


8709 


8S29 


8948 


9068 


9188 


9308 


9428 


9548 


9667 


9787 


120 


363 


9907 


*0026 


*oi46 


*0265 


*03S5 


*0504 


♦0624 


*0743 


*oS63 


♦0982 


119 


364 


561101 


I22I 


1340 


1459 


1578 


1698 


1817 


1936 


2055 


2174 


119 


365 


562293 


2412 


2531 


2650 


2769 


2887 


3006 


3125 


3244 


3362 


119 


366 


34S1 


3600 


3718 


3837 


3955 


4074 


4192 


43" 


4429 


4548 


119 


367 


4666 


47S4 


4903 


5021 


5139 


5257 


5376 


5494 


5612 


5730 


118 


368 


5848 


5966 


6084 


6202 


6320 


6437 


6555 


6673 


6791 


6909 


118 


369 


7026 


7144 


7262 


7379 


7497 


7614 


7732 


7849 


7967 


80S4 


118 


370 


568202 


8319 


8436 


8554 


8671 


8788 


8905 


9023 


9140 


*9257 


117 


371 


9374 


9491 


9608 


9725 


9842 


9959 


*oo76 


*oi93 


*0309 


*0426 


117 


372 


570543 


0660 


0776 


0893 


lOIO 


1126 


1243 


1359 


1476 


1592 


117 


373 


1709 


1S25 


1942 


2058 


2174 


2291 


2407 


2523 


2639 


2755 


116 


374 


2872 


29S8 


3104 


3220 


3336 


3452 


3568 


36S4 


3S00 


3915 


116 


375 


574031 


4147 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


116 


376 


5188 


5303 


5419 


5534 


5650 


5765 


5880 


5996 


6111 


6226 


115 


377 


6341 


6457 


6572 


6687 


6802 


6917 


7032 


7147 


7262 


7377 


115 


378 


7492 


7607 


7722 


7836 


7951 


S066 


8181 


8295 


8410 


8525 


"5 


379 


8639 


8754 


8868 


8983 


9097 


9212 


9326 


9441 


9555 


9669 


114 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




128 


13 


26 


38 


51 


64 


77 


90 


102 


115 


128 




127 


13 


25 


38 


51 


64 


76 


89 


102 


114 


127 




126 


13 


25 


38 


50 


63 


76 


88 


lOI 


"3 


126 


"5 


13 


25 


38 


50 


63 


75 


88 


100 


113 


125 


< 


124 


12 


25 


37 


50 


62 


74 


ll 


9i 


112 


124 


p^ 


123 


12 


25 


37 


49 


62 


74 


86 


9! 


III 


123 




122 


12 


24 


37 


49 


61 


73 


85 


98 


no 


122 


CM 


121 


12 


24 


36 


48 


61 


73 


85 


97 


109 


121 





120 


12 


24 


36 


48 


60 


72 


84 


96 


108 


120 


Oi 
^ 


119 


12 


24 


36 


48 


60 


71 


^3 


95 


107 


iig 




118 


12 


24 


35 


47 


59 


71 


83 


94 


106 


118 




117 


12 


23 


35 


47 


59 


70 


f^ 


94 


105 


117 




H6 


12 


23 


35 


46 


58 


70 


81 


93 


104 


116 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



27s 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


380 


579784 


9898 


*OOI2 


*OI26 


*024I 


*o355 


♦0469 


*o583 


*o697 


*o8ii 


114 


3^' 


5S0925 


1039 


1 153 


1267 


I38I 


1495 


1608 


1722 


1836 


1950 


114 


382 


2063 


2177 


2291 


2404 


2518 


2631 


2745 


2858 


2972 


3085 


114 


383 


3199 


3312 


3426 


3539 


3652 


3765 


3879 


3992 


4105 


4218 


113 


384 


4331 


4444 


4557 


4670 


4783 


4896 


5009 


5122 


5235 


5348 


113 


385 


585461 


5574 


5686 


5799 


5912 


6024 


6137 


6250 


6362 


6475 


"3 


386 


6587 


6700 


6812 


6925 


7037 


7149 


7262 


7374 


74S6 


7599 


112 


387 


7711 


7823 


7935 


8047 


8160 


8272 


8384 


8496 


8608 


8720 


112 


388 


8832 


8944 


9056 


9167 


9279 


9391 


9503 


9615 


9726 


9838 


112 


389 


9950 


*oo6i 


*oi73 


*0284 


*0396 


*0507 


*o6i9 


*0730 


♦0842 


*o953 


112 


390 


591065 


1176 


1287 


1399 


1510 


1621 


1732 


1843 


1955 


2066 


III 


391 


2177 


2288 


2399 


2510 


2621 


2732 


2843 


2954 


3064 


3175 


III 


392 


3286 


3397 


3508 


361S 


3729 


3840 


3950 


4061 


4171 


4282 


III 


393 


4393 


4503 


4614 


4724 


4834 


4945 


5055 


5165 


5276 


5386 


1 10 


394 


5496 


5606 


5717 


5827 


5937 


6047 


6157 


6267 


6377 


64S7 


110 


395 


596597 


6707 


6817 


6927 


7037 


7146 


7256 


7366 


7476 


75S6 


110 


396 


7695 


7805 


7914 


8024 


8134 


8243 


8353 


8462 


8572 


8681 


no 


397 


8791 


8900 


9009 


9119 


9228 


9337 


9446 


.9556 


9665 


9774 


109 


398 


9883 


9992 


*OIOI 


*02I0 


♦0319 


*o428 


*0537 


♦0646 


*o755 


*oS64 


109 


399 


600973 


1082 


1191 


1299 


1408 


1517 


1625 


1734 


1843 


1951 


109 


400 


602060 


2169 


2277 


2386 


2494 


2603 


2711 


2S19 


2928 


3036 


108 


401 


3144 


3253 


3361 


3469 


3577 


3686 


3794 


3902 


4010 


4118 


108 


402 


4226 


4334 


4442 


4550 


4658 


4766 


4874 


4982 


5089 


5197 


108 


403 


5305 


5413 


5521 


5628 


5736 


5844 


5951 


6059 


6166 


6274 


108 


404 


6381 


6489 


6596 


6704 


681 1 


6919 


7026 


7133 


7241 


7348 


107 


405 


607455 


7562 


7669 


7777 


78S4 


7991 


8098 


8205 


8312 


8419 


107 


406 


8526 


8633 


8740 


8847 


8954 


9061 


9167 


9274 


9381 


9488 


107 


407 


9594 


9701 


9S08 


9914 


*002I 


*OI28 


*0234 


*034l 


*0447 


*0554 


107 


408 


610660 


0767 


0873 


0979 


1086 


1192 


1298 


1405 


1511 


1617 


106 


409 


1723 


1S29 


1936 


2042 


2148 


2254 


2360 


2466 


2572 


2678 


106 


410 


6127S4 


2890 


2996 


3102 


3207 


3313 


3419 


3525 


3630 


3736 


106 


411 


3842 


3947 


4053 


4159 


4264 


4370 


4475 


45S1 


4686 


4792 


106 


412 


4897 


5003 


5108 


5213 


5319 


5424 


5529 


5634 


5740 


5845 


105 


413 


5950 


6055 


6160 


6265 


6370 


6476 


65S1 


6686 


6790 


6895 


105 


414 


7000 


7105 


7210 


7315 


7420 


7525 


7629 


7734 


7839 


7943 


105 


415 


61S048 


8153 


8257 


8362 


8466 


8571 


8676 


8780 


88S4 


8989 


105 


416 


9093 


9198 


9302 


9406 


95" 


9615 


9719 


9824 


9928 


*0O32 


104 


t'Z 


620136 


0240 


0344 


0448 


0552 


0656 


0760 


0864 


096S 


1072 


104 


418 


1 176 


1280 


1384 


1488 


1592 


1695 


1799 


1903 


2007 


2110 


104 


419 


2214 


2318 


2421 


2525 


2628 


2732 


2835 


2939 


3042 


3146 


104 


N. 


DiflF. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




"5 


12 


23 


35 


46 


58 


69 


81 


92 


104 


"5 




114 


II 


23 


34 


46 


57 


68 


80 


91 


103 


X14 


en 


"3 


II 


23 


34 


45 


57 


68 


79 


90 


102 


"3 


H 


112 


II 


22 


34 


45 


56 


67 


78 


90 


lOI 


113 


< 


III 


II 


22 


33 


44 


56 


67 


78 




100 


III 


no 


II 


22 


33 


44 


55 


66 


77 


88 


99 


no 




log 


II 


22 


33 


44 


55 


65 


76 


87 


98 


log 





108 


II 


22 


32 


43 


54 


65 


76 


86 


97 


108 


107 


II 


21 


32 


43 


54 


64 


75 


86 


96 


107 


106 


II 


21 


32 


42 


53 


64 


74 


f5 


95 


106 




105 


II 


21 


32 


42 


53 


63 


74 


84 


95 


105 




104 


10 


21 


31 


42 


52 


62 


73 


!3 


94 


104 




103 


10 


21 


31 


41 


52 


62 


72 


82 


93 


103 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



276 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N. 
420 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


623249 


3353 


3456 


3559 


3663 


3766 


3869 


3973 


4076 


4179 


103 


421 


4282 


4385 


4488 


4591 


4695 


4798 


4901 


5004 


5107 


5210 


103 


422 


5312 


5415 


551S 


5621 


5724 


5827 


5929 


6032 


6135 


6238 


103 


423 


6340 


6443 


6546 


6648 


6751 


6S53 


6956 


7058 


7161 


7263 


103 


424 


7366 


7468 


7571 


7673 


7775 


7878 


7980 


80S2 


81S5 


82S7 


102 


425 


628389 


8491 


8593 


8695 


8797 


8900 


9002 


9104 


9206 


9308 


102 


426 


9410 


9512 


9613 


9715 


9817 


9919 


*002I 


*0I23 


*0224 


♦0326 


102 


427 


630428 


0530 


0631 


0733 


0S35 


0936 


1038 


1139 


I24I 


1342 


102 


428 


1444 


1545 


1647 


1748 


1849 


1951 


2052 


2153 


^^il 


2356 


lOI 


429 


2457 


2559 


2660 


2761 


2862 


2963 


3064 


3165 


3266 


3367 


lOI 


430 


633468 


3569 


3670 


3771 


3872 


3973 


4074 


4175 


4276 


4376 


lOI 


431 


4477 


4578 


4679 


4779 


4880 


4981 


5081 


5182 


5283 


P^i 


lOI 


432 


5484 


5584 


5685 


5785 


5886 


59S6 


6087 


6187 


6287 


63S8 


100 


433 


6488 


6588 


6688 


6789 


6889 


6989 


7089 


7189 


7290 


7390 


100 


434 


7490 


7590 


7690 


7790 


7890 


7990 


8090 


8190 


8290 


83S9 


100 


435 


638489 


8589 


8689 


8789 


8888 


8988 


9088 


9188 


*9^§7 


9387 


100 


436 


9486 


9586 


9686 


9785 


9885 


9984 


*oo84 


*oi83 


*0283 


♦0382 


99 


437 


640481 


0581 


0680 


0779 


0879 


0978 


1077 


1177 


1276 


'H^ 


99 


438 


1474 


1573 


1672 


1771 


1S71 


1970 


2069 


2168 


2267 


2366 


99 


439 


2465 


2563 


2662 


2761 


2860 


2959 


3058 


3156 


3255 


3354 


99 


440 


643453 


3551 


3650 


3749 


3847 


3946 


4044 


4143 


4242 


4340 


^t 


441 


4439 


4537 


4636 


4734 


4832 


4931 


5029 


5127 


5226 


^^^i 


9^ 


442 


5422 


5521 


5619 


5717 


5815 


5913 


6011 


6110 


6208 


6306 


98 


443 


6404 


6502 


6600 


6698 


6796 


6894 


6992 


70S9 


7187 


7285 


9^ 


444 


7383 


74S1 


7579 


7676 


7774 


7872 


7969 


8067 


8165 


8262 


98 


445 


648360 


8458 


8555 


8653 


8750 


8S48 


8945 


9043 


9140 


9237 


97 


446 


9335 


9432 


9530 


9627 


9724 


9821 


9919 


*ooi6 


*oii3 


*02IO 


97 


447 


650308 


0405 


0502 


0599 


0696 


0793 


0890 


0987 


1084 


I18I 


97 


448 


1278 


1375 


1472 


1569 


1666 


1762 


'§59 


1956 


2053 


2150 


97 


449 


2246 


2343 


2440 


2536 


2633 


2730 


2826 


2923 


3019 


31 16 


97 


450 


653213 


3309 


3405 


3502 


3598 


3695 


3791 


3888 


3984 


4080 


9^ 


451 


4177 


4273 


4369 


4465 


4562 


4658 


4754 


4850 


4946 


5042 


96 


452 


5138 


5235 


5331 


5427 


5523 5619 


5715 


5810 


5906 


6002 96 1 


453 


6098 


6194 


6290 


6386 


6482 


6577 


6673 


6769 


6864 


6960 


96 


454 


7056 


7152 


7247 


7343 


7438 


7534 


7629 


7725 


7820 


7916 


96 


455 


658011 


8107 


8202 


8298 


8393 


8488 


8584 


8679 


8774 


8870 


95 


456 


8965 


9060 


9155 


9250 


9346 


9441 


9536 


9631 


9726 


9821 


95 


457 


9916 


*OOII 


*oio6 


*020I 


*0296 


*039i 


*0486 


*058i 


*o676 


*077i 


95 


458 


660865 


0960 


1055 


1150 


1245 


1339 


1434 


1529 


1623 


1718 


95 


459 


1813 


1907 


2002 


2096 


2191 


2286 


2380 


2475 


2569 


2663 


95 


460 


662758 


2852 


2947 


3041 


3135 


3230 


3324 


3418 


3512 


3607 


94 


461 


3701 


3795 


38S9 


3983 


4078 


4172 


4266 


4360 


4454 


4548 


94 


462 


4642 


4736 4830 


4924 


5018 


5112 


5206 


5299 


5393 


5487 


94 


463 


5581 


5675 57(>9 


5862 


5956 


6050 


6143 


6237 


6331 


6424 


94 


464 


6518 


6612 6705 


6799 


6892 


6986 


7079 


7173 


7266 


7360 


94 


N. 


Diff. 


Z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




104 


10 


21 


31 


42 


52 


62 


73 


83 


94 


104 


M 

H 


103 


10 


21 


31 


41 


52 


62 


72 


82 


93 


103 


102 


10 


20 


31 


41 


51 


61 


71 


82 


92 


102 


lOI 


10 


20 


30 


40 


51 


61 


71 


81 


91 


lOI 


cu 


100 


10 


20 


30 


40 


50 


60 


70 


80 


90 


100 


a, 

oi 


99 


10 


20 


30 


40 


50 


59 1 69 


79 


89 


9i 


98 


10 


20 


29 


39 


49 


59 


69 


78 


88 


98 


97 


10 


19 


29 


39 


49 


58 


68 


78 


87 


^l 


Oi 


96 


10 


19 


29 


38 


48 


58 


67 


77 


86 


96 




95 


10 


19 


29 


38 


48 


57 


67 


76 


86 


95 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



277 



table; VII.— logarithms of numbers. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


465 


667453 


7546 


7640 


7733 


7826 


7920 


8013 


8106 


8199 


8293 


93 


466 


S386 


8479 


8572 


8665 


8759 


8852 


8945 


9038 


9131 


9224 


93 


467 


^ 9317 


9410 


9503 


9596 


9689 


9782 


9875 


9967 


*oo6o 


*oi53 


93 


468 


670246 


0339 


0431 


0524 


0617 


0710 


0802 


0895 


0988 


1080 


93 


469 


1173 


1265 


1358 


145 1 


1543 


1636 


1728 


1821 


1913 


2005 


93 


470 


672098 


2190 


2283 


2375 


2467 


2560 


2652 


2744 


2836 


2929 


92 


471 


3021 


3113 


3205 


3297 


3390 


3482 


3574 


3666 


3758 


3850 


92 


472 


3942 


4034 


4126 


4218 


4310 


4402 


4494 


4586 


4677 


4769 


92 


473 


4861 


4953 


5045 


5137 


5228 


5320 


5412 


5503 


5595 


5687 


92 


474 


^ 5778 


5S70 


5962 


6053 


6145 


6236 


6328 


6419 


651 1 


6602 


92 


475 


676694 


67S5 


6876 


6968 


7059 


7151 


7242 


7333 


7424 


7516 


91 


476 


7607 


7698 


7789 


7S81 


7972 


8063 


8154 


8245 


8336 


8427 


91 


477 


8518 


8609 


8700 


8791 


8882 


8973 


9064 


9155 


9246 


9337 


91 


478 


9428 


9519 


9610 


9700 


9791 


9882 


9973 


*oo63 


*oi54 


*0245 


91 


479 


680336 


0426 


0517 


0607 


0698 


0789 


0879 


0970 


1060 


1 151 


91 


480 


681 241 


1332 


1422 


1513 


1603 


1693 


17S4 


1874 


1964 


2055 


90 


481 


2145 


2235 


2326 


2416 


2506 


2596 


2686 


2777 


2867 


2957 


90 


482 


3047 


3137 


3227 


3317 


3407 


3497 


3587 


3677 


3767 


3857 


90 


483 


3947 


4037 


4127 


4217 


4307 


4396 


4486 


4576 


4666 


4756 


90 


484 


^4845 


4935 


5025 


5114 


5204 


5294 


5383 


5473 


5563 


5652 


90 


485 


685742 


5831 


5921 


6010 


6100 


61S9 


6279 


6368 


6458 


6547 


89 


486 


6636 


6726 


6815 


6904 


6994 


70S3 


7172 


7261 


7351 


7440 


89 


"^ll 


7529 


7618 


7707 


7796 


7886 


7975 


8064 


8153 


8242 


8331 


89 


488 


8420 


8509 


8598 


8687 


8776 


SS65 


8953 


9042 


9131 


9220 


89 


489 


9309 


9398 


9486 


9575 


9664 


9753 


9841 


9930 


*ooi9 


*oio7 


89 


490 


690196 


0285 


0373 


0462 


0550 


0639 


0728 


0816 


0905 


°993 


89 


491 


1081 


1 170 


1258 


1347 


1435 


1524 


1612 


1700 


1789 


1877 


88 


492 


1965 


2053 


2142 


2230 


2318 


2406 


2494 


2583 


2671 


2759 


88 


493 


2847 


2935 


3023 


3111 


3199 


3287 


3375 


3463 


3551 


3639 


88 


494 


^ 3p7 


3S15 


3903 


3991 


4078 


4166 


4254 


4342 


4430 


4517 


88 


495 


694605 


4693 


4781 


4868 


4956 


5044 


5131 


5219 


5307 


5394 


88 


496 


5482 


5569 


5657 


5744 


5S32 


5919 


6007 


6094 


61S2 


6269 


87 


497 


6356 


6444 


6531 


6618 


6706 


^793 


6880 


6968 


7055 


7142 


87 


498 


7229 


7317 


7404 


7491 


7578 


7665 


7752 


7839 


7926 


8014 


87 


499 


8101 


8188 


8275 


8362 


8449 


8535 


8622 


8709 


8796 


8883 


87 


500 


69S970 


9057 


9144 


9231 


9317 


9404 


9491 


9578 


9664 


9751 


87 


501 


9838 


9924 


*00II 


*0098 


*oi84 


*027I 


*035S 


*0444 


*053i 


*o6i7 


Sj 


502 


700704 0790 


0S77 


0963 


1050 


1 136 


1222 


1309 


1395 


1482 


86 


503 


1568 


1654 


1741 


1827 


1913 


1999 


2086 


2172 


2258 


2344 


86 


504 


2431 


2517 


2603 


2689 


2775 


2861 


2947 


3033 


3119 


3205 


86 


50s 


703291 


3377 


3463 


3549 


3635 


3721 


3807 


3893 


3979 


4065 


86 


506 


4151 


4236 


4322 


4408 


4494 


4579 


4665 


4751 


4837 


4922 


86 


507 


5008 


5094 


5179 


5265 


5350 


5436 


5522 


5607 


5693 


5778 


86 


508 


5864 


5949 


6035 


6l20 


6206 


6291 


6376 


6462 


6547 


6632 


85 


509 


6718 


6803 


6888 


6974 


7059 


7144 


7229 


7315 


7400 


7485 


85 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




94 


9 


19 


28 


38 


47 


56 


66 


75 


85 


94 


W 

H 

Oh 


93 


9 


19 


28 


37 


47 


56 


65 


74 


84 


93 


92 


9 


18 


28 


37 


46 


55 


64 


74 


83 


92 


< 


91 


9 


18 


27 


36 


46 


55 


64 


73 


82 


91 


a. 


90 


9 


18 


27 


36 


45 


54 


63 


72 


81 


90 


oi 


!9 


9 


18 


27 


36 


45 


53 


62 


71 


80 


89 





88 


9 


18 


26 


35 


44 


53 


62 


70 


79 


88 


Pi 


87 


9 


17 


26 


35 


44 


52 


61 


70 


78 


87 


Pa 


86 


9 


17 


26 


34 


43 


52 


60 


69 


77 


86 1 




85 


9 


17 


26 


34 


43 


51 


60 


68 


77 


85! 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



278 







table; VII.— logarithms of numbers. 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


510 


707570 


7655 


7740 


7826 


791 1 


7996 


8081 


8166 


8251 


8336 


85 


5" 


8421 


8506 


8591 


8676 


8761 


8846 


8931 


9015 


9100 


9185 


85 


512 


9270 


9355 


9440 


9524 


9609 


9694 


9779 


9863 


9948 


*oo33 


85 


513 


7IOII7 


0202 


0287 


0371 


0456 


0540 


0625 


0710 


0794 


0S79 


85 


514 


0963 


1048 


1132 


1217 


1301 


1385 


1470 


1554 


1639 


1723 


84 


515 


7I1S07 


1892 


1976 


2060 


2144 


2229 


2313 


2397 


2481 


2566 


84 


516 


2650 


2734 


2818 


2902 


29S6 


3070 


3154 


3238 


3323 


3407 


84 


5^7 


3491 


3575 


3659 


3742 


3826 


3910 


3994 


4078 


4162 


4246 


84 


518 


4330 


4414 


4497 


4581 


4665 


4749 


4833 


4916 


5000 


5084 


84 


519 


5167 


5251 


5335 


5418 


5502 


55S6 


5669 


5753 


5836 


5920 


84 


520 


716003 


6087 


6170 


6254 


6337 


6421 


6504 


6588 


6671 


6754 


83 


521 


6S3S 


6921 


7004 


708S 


7171 


7254 


7338 


7421 


7504 


75S7 


83 


522 


7671 


7754 


7837 


7920 


8003 


8086 


8169 


8253 


8336 


8419 


83 


523 


8502 


85S5 


8668 


8731 


8S34 


8917 


9000 


9083 


9165 


9248 


83 


524 


9331 


9414 


9497 


95S0 


9663 


9745 


9828 


991 1 


9994 


*oo77 


83 


525 


720159 


0242 


0325 


0407 


0490 


0573 


0655 


0738 


0821 


0903 


83 


526 


0986 


1068 


1151 


1233 


1316 


1398 


148 1 


1563 


1646 


172S 


82 


527 


I8II 


1893 


1975 


2058 


2140 


2222. 


2305 


2387 


2469 


2552 


82 


528 


2634 


2716 


2798 


2881 


2963 


3045 


3127 


3209 


3291 


3374 


82 


529 


3456 


3538 


3620 


3702 


3784 


3866 


3948 


4030 


4112 


4194 


82 


530 


724276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


4931 


5013 


82 


531 


5095 


5176 


5258 


5340 


5422 


5503 


5585 


5667 


5748 


5830 


82 


532 


5912 


5993 


6075 


6156 


6238 


6320 


6401 


6483 


6564 


6646 


82 


533 


6727 


6S09 


6S90 


6972 


7053 


7134 


7216 


7297 


7379 


7460 


81 


534 


7541 


7623 


7704 


77S5 


7S66 


7948 


8029 


8110 


8191 


8273 


81 


535 


728354 


8435 


S516 


8597 


8678 


8759 


8841 


8922 


9003 


9084 


8i 


536 


9165 


9246 


.9327 


9408 


94S9 


9570 


9651 


9732 


9813 


9S93 


81 


537 


9974 


*oo55 


*oi36 


*02I7 


*029S 


*o378 


*0459 


*0540 


*062I 


*0702 


81 


538 


730782 


0863 


0944 


1024 


1 105 


1 186 


1266 


1347 


1428 


1508 


8i 


539 


1589 


1669 


1750 


1S30 


1911 


1991 


2072 


2152 


2233 


2313 


81 


540 


732394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 


3037 


3II7 


80 


541 


3197 


3278 


3358 


3438 


3518 


3598 


3679 


3759 


3839 


3919 


80 


542 


3999 


4079 


4160 


4240 


4320 


4400 


4480 


4560 


4640 


4720 


80 


543 


4800 


4880 


4960 


5040 


5120 


5200 


5279 


5359 


5439 


5519 


80 


544 


5599 


5679 


5759 


5838 


5918 


599S 


6078 


6157 


6237 


6317 


80 


545 


736397 


6476 


6556 


6635 


6715 


6795 


6874 


6954 


7034 


7II3 


80 


546 


7193 


7272 


7352 


7431 


751 1 


7590 


7670 


7749 


7829 


7908 


79 


547 


7987 


8067 


8146 


8225 


8305 


8384 


8463 


8543 


8622 


8701 


79 


548 


8781 


8860 


8939 


90IS 


9097 


9177 


9256 


^9335 


9414 


9493 


79 


549 


9572 


9651 


9731 


9810 


9S89 


9968 


*oo47 


*OI26 


*0205 


*0284 


79 


550 


740363 


0442 


0521 


0600 


0678 


0757 


0836 


0915 


0994 


1073 


79 


551 


1152 


1230 


1309 


1388 


1467 


1546 


1624 


1703 


1782 


i860 


79 


552 


1939 


2018 


2096 


2175 


2254 


2332 


241 1 


2489 


2568 


2647 


79 


553 


2725 


2804 


2882 


2961 


3039 


3118 


3196 


3275 


3353 


3431 


78 


554 


3510 


3588 


3667 


3745 


3823 


3902 


3980 


4058 


4136 


4215 


78 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 
86 


m 


86 


9 


17 


26 


34 


43 


52 


60 


69 


77 


^ 


85 




17 


26 


34 


43 


51 


60 


68 


77 


?5 


< 


84 


8 


17 


25 


34 


42 


50 


59 


67 


76 


84 


^ 


83 


8 


17 


25 


33 


42 


50 


58 


66 


75 


83 




82 


8 


16 


25 


33 


41 


49 


57 


66 


74 


82 


cu 


81 


8 


16 


24 


32 


41 


49 


57 


65 


73 


81 





80 


8 


16 


24 


32 


40 


48 


56 


64 


72 


80 


79 


8 


16 


24 


32 


40 


47 


55 


63 


71 


79 




Diff. 


I 


2 


3 


1 
4 


5 


6 


7 


8 


9 


Diff. 



279 







TABLE VII.— LOGARITHMS OF NUMBERS. 






N. 
555 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


744293 


4371 


4449 


4528 


4606 


4684 


4762 


4840 


4919 


4997 


78 


556 


5075 


5153 


5231 


5309 


5387 


5465 


5543 


5621 


5699 


5777 


78 


557 


5855 


5933 


601 1 


60S9 


6167 


6245 


6323 


6401 


6479 


6556 


78 


558 


6634 


6712 


6790 


6868 


6945 


7023 


7101 


7179 


7256 


7334 


78 


559 


7412 


7489 


7567 


7645 


7722 


7800 


7878 


7955 


8033 


8110 


78 


560 


748 1S8 


8266 


8343 


8421 


8498 


8576 


8653 


8731 


8808 


8885 


77 


561 


8963 


9040 


9118 


9195 


9272 


9350 


9427 


9504 


9582 


9659 


77 


562 


9736 


9814 


9891 


9968 


*oo45 


*OI23 


*0200 


*0277 


*0354 


*043i 


77 


563 


750508 


0586 


0663 


0740 


0817 


0894 


0971 


1048 


1125 


1202 


77 


564 


1279 


1356 


1433 


1510 


1587 


1664 


I74I 


1818 


1895 


1972 


77 


5^1 


752048 


2125 


2202 


2279 


2356 


2433 


2509 


2586 


2663 


2740 


77 


566 


2816 


2S93 


2970 


3047 


3123 


3200 


3277 


3353 


3430 


3506 


77 


55Z 


3583 


3660 


3736 


3813 


3S89 


3966 


4042 


4119 


4195 


4272 


77 


568 


4348 


4425 


4501 


4578 


4654 


4730 


4807 


4883 


4960 


5036 


76 


569 


5112 


5189 


5265 


5341 


5417 


5494 


5570 


5646 


5722 


5799 


76 


570 


755875 


5951 


6027 


6103 


6j8o 


6256 


6332 


6408 


6484 


6560 


76 


571 


6636 


6712 


6788 


6864 


6940 


7016 


7092 


7168 


7244 


7320 


76 


572 


7396 


7472 


7548 


7624 


7700 


7775 


7851 


7927 


8003 


8079 


76 


573 


8155 


8230 


8306 


8382 


8458 


8533 


8609 


8685 


8761 


8836 


76 


574 


8912 


8988 


9063 


9139 


9214 


9290 


9366 


9441 


9517 


9592 


76 


575 


759668 


9743 


9S19 


9S94 


9970 


*oo45 


*OI2I 


♦0196 


*0272 


*0347 


75 


576 


760422 


0498 


0573 


0649 


0724 


0799 


0875 


0950 


1025 


IIOI 


75 


577 


1 1 76 


1 25 1 


1326 


1402 


1477 


1552 


1627 


1702 


I77S 


1853 


75 


578 


1928 


2003 


2078 


2153 


2228 


2303 


2378 


2453 


2529 


2604 


75 


579 


2679 


2754 


2829 


2904 


2978 


3053 


3128 


3203 


3278 


3353 


75 


580 


763428 


3503 


3578 


3653 


3727 


3802. 


3877 


3952 


4027 


4101 


75 


5^' 


4176 


4251 


4326 


4400 


4475 


4550 


4624 


4699 


4774 


4848 


75 


5^* 


4923 


4998 


5072 


5147 


5221 


5296 


5370 


5445 


5520 


5594 


75 


5?3 


5669 


5743 


5818 


5892 


5966 


6041 


6115 


6190 


6264 


6338 


74 


584 


6413 


6487 


6562 


6636 


6710 


67S5 


6859 


6933 


7007 


7082 


74 


5fl 


767156 


7230 


7304 


7379 


7453 


7527 


7601 


7675 


7749 


7823 


74 


586 


7898 


7972 


8046 


8120 


8194 


8268 


8342 


8416 


8490 


8564 


74 


^ll 


8638 


8712 


8786 


8860 


8934 


9008 


9082 


9156 


9230 


9303 


74 


588 


9377 


9451 


9525 


9599 


9673 


9746 


9820 


9894 


9968 


*0O42 


74 


589 


7701 15 


0189 


0263 


0336 


0410 


0484 


0557 


0631 


0705 


0778 


74 


590 


770852 


0926 


0999 


1073 


1 146 


1220 


1293 


1367 


1440 


I5I4 


74 


591 


1587 


166 1 


1734 


1808 


1881 


1955 


2028 


2102 


2175 


2248 


73 


592 


2322 


2395 


2468 


2542 


2615 


2688 


2762 


2835 


2908 


2981 


73 


593 


3055 


3128 


3201 


3274 


3348 


3421 


3494 


3567 


3640 


3713 


73 


594 


3786 


3860 


3933 


4006 


4079 


4152 


4225 


4298 


4371 


4444 


73 


595 


774517 


4590 


4663 


4736 


4809 


4882 


4955 


5028 


5100 


5173 


73 


596 


5246 


5319 


5392 


5465 


5538 


5610 


5683 


5756 


5829 


5902 


73 


597 


5974 


6047 


6120 


6193 


6265 


6338 


641 1 


64S3 


6556 


6629 


73 


598 


6701 


6774 


6846 


6919 


6992 


7064 


7137 


7209 


7282 


7354 


73 


599 


7427 


7499 


7572 


7644 


7717 


7789 


7862 


7934 


8006 


8079 


72 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




78 


8 


16 


23 


31 


39 


47 


55 


62 


70 


78 


Di 


77 


8 


15 


23 


31 


39 


46 


54 


62 


69 


77 


< 


76 


8 


15 


23 


30 


38 


46 


53 


61 


68 


76 


0< 


75 


8 


15 


23 


30 


38 


45 


53 


60 


68 


75 


d 


74 


7 


15 


22 


30 


37 


44 


52 


59 


67 


74 


73 


7 


15 


22 


29 


37 


44 


51 


58 


66 


73 


0. 


72 


7 


14 


22 


29 


36 


43 


50 


58 


65 


72 
Diff. 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 



280 







table; VII.— logarithms of 


NUMB] 


ERS. 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


600 


778151 


8224 


8296 


8368 


8441 


8513 


8585 


8658 


8730 


8802 


72 


601 


8874 


8947 


9019 


9091 


9163 


9236 


9308 


9380 


9452 


9524 


72 


602 


9596 


9669 


9741 


9813 


9885 


9957 


*0029 


*0I0I 


*oi73 


*0245 


72 


603 


780317 


0389 


0461 


0533 


0605 


0677 


0749 


0821 


0893 


0965 


72 


604 


1037 


1 109 


1181 


1253 


1324 


1396 


1468 


1540 


1612 


1684 


72 


605 


781755 


IS27 


1899 


197 1 


2042 


2114 


2186 


2258 


2329 


2401 


72 


606 


2473 


2544 


2616 


2688 


2759 


2831 


2902 


2974 


3046 


3117 


72 


607 


31S9 


3260 


3332 


3403 


3475 


3546 


3618 


36S9 


3761 


3832 


71 


608 


3904 


3975 


4046 


4118 


41S9 


4261 


4332 


4403 


4475 


4546 


71 


609 


4617 


4689 


4760 


4S31 


4902 


4974 


5°45 


5II6 


5187 


5259 


71 


610 


785330 


5401 


5472 


5543 


5615 


56S6 


5757 


5828 


5899 


5970 


71 


611 


6041 


6112 


6183 


6254 


6325 


6396 


6467 


6538 


6609 


66S0 


71 


612 


6751 


6822 


6S93 


6964 


7035 


7106 


7177 


7248 


7319 


7390 


71 


613 


7460 


7531 


7602 


7673 


7744 


7815 


7885 


7956 


8027 


8098 


71 


614 


8168 


8239 


8310 


8381 


8451 


8522 


8593 


8663 


8734 


8804 


71 


615 


788875 


8946 


9016 


9087 


9157 


9228 


9299 


9369 


9440 


9510 


71 


616 


9581 


9651 


9722 


9792 


9863 


9933 


*ooo4 


*0074 


*oi44 


*02I5 


70 


617 


790285 


0356 


0426 


0496 


0567 


0637 


0707 


0778 


0848 


0918 


70 


618 


09S8 


1059 


1 1 29 


1199 


1269 


1340 


1410 


1480 


1550 


1620 


70 


6ig 


169 1 


1761 


1831 


1901 


1971 


2041 


2111 


2181 


2252 


2322 


70 


620 


792392 


2462 


2532 


2602 


2672 


2742 


2812 


2882 


2952 


3022 


70 


621 


3092 


3162 


3231 


3301 


3371 


3441 


35" 


3581 


3651 


3721 


70 


622 


3790 


3860 


3930 


4000 


4070 


4139 


4209 


4279 


4349 


4418 


70 


623 


44S8 


4558 


4627 


4697 4767 


4836 


4906 


4976 


5045 


5II5 


70 


624 


51S5 


5254 


5324 


5393 


5463 


5532 


5602 


5672 


5741 


58H 


70 


625 


795S80 


5949 


6019 


6088 


6158 


6227 


6297 


6366 


6436 


6505 


69 


626 


6574 


6644 


6713 


6782 


6852 


6921 


6990 


7060 


7129 


7198 


^9 


627 


7268 


7337 


7406 


7475 


7545 


7614 


7683 


7752 


7821 


7S90 


69 


628 


7960 


8029 


8098 


8167 


8236 


8305 


8374 


8443 


8513 


8582 


69 


629 


8651 


8720 


8789 


8858 


8927 


8996 


9065 


9134 


9203 


9272 


69 


630 


799341 


9409 


9478 


9547 


9616 


9685 


9754 


9823 


9892 


9961 


^9 


631 


800029 


0098 


oib7 


0236 


0305 


0373 


0442 


051 1 


05S0 


0648 


69 


632 


0717 


0786 


0854 


0923 


0992 


106 1 


1129 


1 198 


1266 


1335 


69 


633 


1404 


1472 


1541 


1609 


1678 


1747 


1815 


1884 


1952 


2021 


69 


634 


2089 


2158 


2226 


2295 


2363 


2432 


2500 


2568 


2637 


2705 


68 


635 


802774 


2842 


2910 


2979 


3047 


3116 


3184 


3252 


3321 


3389 


68 


636 


3457 


3525 


3594 


3662 


3730 


3798 


3867 


3935 


4003 


4071 


68 


637 


4139 


4208 


4276 


4344 


4412 


44S0 


4548 


4616 


4685 


4753 


68 


638 


4821 


4889 


4957 


5025 


5093 


5161 


5229 


5297 


5365 


5433 


68 


639 


5501 


5569 


5637 


5705 


5773 


5841 


5908 


5976 


6044 


6112 


68 


640 


806 I So 


6248 


6316 


6384 


6451 


6519 


6587 


6655 


6723 


6790 


68 


641 


6S58 


6926 


6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 


68 


642 


7535 


7603 


7670 


7738 


7806 


7873 


7941 


8008 


8076 


8143 


68 


643 


8211 


8279 


8346 


8414 


8481 


8549 


8616 


8684 


8751 


8818 


67 


644 


8886 


8953 


9021 


9088 


9156 


9223 


9290 


9358 


9425 


,9492 


67 


645 


809560 


9627 


9694 


9762 


9829 


9896 


9964 


*0O3i 


♦0098 


*oi65 


67 


646 


810233 


0300 


0367 


0434 


0501 


0569 


0636 


0703 


0770 


0837 


67 


647 


0904 


0971 


1039 


1 106 


1 173 


1240 


1307 


1374 


1441 


1508 


67 


648 


1575 


1642 


1709 


1776 


1843 


1910 


1977 


2044 


2111 


2178 


67 


649 


2245 


2312 


2379 


2445 


2512 


2579 


2646 


2713 


2780 


2847 


67 


N. 


Diff. 


I 2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


03 


73 


7 15 


22 


29 


37 


44 


51 


5^ 


66 


73 


H 


72 


7 14 


22 


29 


36 


43 


50 


58 


65 


72 


Oi 


71 


7 


14 


21 


28 


36 


43 


50 


57 


64 


71 




70 


7 


14 


21 


28 


35 


42 


49 


56 


63 


70 


6 

a, 


a§ I 


14 


21 


28 


35 


41 


48 


55 


62 


^1 


14 


20 


27 


34 


41 


48 


54 


61 


68 
Diff. 




Diff. 1 


2 


3 


4 


5 


6 


7 


8 


9 



281 



TABLE VII.— LOGARITHMS OF NUMBERS. 



N, 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

67 


650 


8129I3 


2980 


3047 


3II4 


3181 


3247 


3314 


3381 


3448 


3514 


651 


3581 


3648 


3714 


3781 


3848 


3914 


3981 


4048 


41 14 


41S1 


67 


652 


4248 


4314 


4381 


4447 


4514 


4581 


4647 


4714 


4780 


4847 


67 


653 


4913 


4980 


5046 


5113 


5179 


5246 


5312 


5378 


5445 


551 1 


66 


654 


5578 


5644 


57" 


5777 


5843 


5910 


5976 


6042 


6109 


6175 


66 


655 


81624I 


6308 


6374 


6440 


6506 


6573 


6639 


6705 


6771 


6838 


66 


656 


6904 


6970 


7036 


7102 


7169 


7235 


7301 


7367 


7433 


7499 


66 


657 


7565 


7631 


7698 


7764 


7830 


7896 


7962. 


8028 


8094 


8160 


66 


658 


8226 


8292 


8358 


8424 


8490 


S556 


8622 


86S8 


8754 


8820 


66 


659 


8885 


8951 


9017 


9083 


9149 


9215 


9281 


9346 


9412 


9478 


66 


660 


819544 


9610 


9676 


9741 


9807 


9S73 


9939 


*ooo4 


♦0070 


♦0136 


66 


661 


820201 


0267 


0333 


0399 


0464 


0530 


0595 


0661 


0727 


0792 


66 


662 


0858 


0924 


0989 


1055 


1 1 20 


1186 


1251 


1317 


13S2 


1448 


66 


663 


I514 


1579 


1645 


1710 


1775 


1841 


1906 


1972 


2037 


2103 


65 


664 


2168 


2233 


2299 


2364 


2430 


2495 


2560 


2626 


2691 


2756 


65 


665 


822822 


2887 


2952 


3018 


30S3 


3148 


3213 


3279 


3344 


3409 


65 


666 


3474 


3539 


3605 


3670 


3735 


3800 


3865 


3930 


3996 


4061 


65 


667 


4126 


4191 


4256 


4321 


4386 


4451 


4516 


45S1 


4646 


4711 


65 


668 


4776 


4841 


4906 


4971 


5036 


5101 


5166 


5231 


5296 


5361 


65 


66g 


5426 


5491 


5556 


5621 


5686 


5751 


5815 


5880 


5945 


6010 


65 


670 


826075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 


65 


671 


6723 


6787 


6852 


6917 


69S1 


7046 


7111 


7175 


7240 


7305 


65 


672 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 


7886 


7951 


65 


673 


8015 


8080 


8144 


8209 


8273 


8338 


8402 


8467 


8531 


8595 


64 


674 


8660 


S724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 


64 


675 


829304 


9368 


9432 


9497 


9561 


9625 


9690 


9754 


9818 


9882 


64 


676 


9947 


*OOII 


*oo75 


*oi39 


*02O4 


*0268 


*0332 


♦0396 


*046o 


*0525 


64 


^l 


830589 


0653 


0717 


0781 


0S45 


0909 


0973 


1037 


1102 


1166 


64 


678 


1230 


1294 


1358 


1422 


i486 


1550 


1614 


1678 


1742 


1806 


64 


679 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


2381 


2445 


64 


680 


832509 


2573 


2637 


2700 


2764 


2828 


2892 


2956 


3020 


3083 


64 


681 


3147 


3211 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


3721 


64 


682 


3784 


3S48 


3912 


3975 


4039 


4103 


4166 


4230 


4294 


4357 


64 


683 


4421 


44S4 


4548 


4bii 


4675 


4739 


4802 


4866 


4929 


4993 


64 


^o^ 


5056 


5120 


5183 


5247 


5310 


5373 


5437 


5500 


5564 


5627 


63 


685 


835691 


5754 


5817 


5S81 


5944 


6007 


6071 


6134 


6197 


6261 


63 


686 


6324 


6387 


6451 


6514 


6577 


6641 


6704 


6767 


6S-,o 


6894 


63 


687 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525 


63 


688 


7588 


7652 


7715 


7778 


7S41 


7904 


7967 


8030 


8093 


8156 


63 


68g 


8219 


8282 


8345 


8408 


8471 


8534 


8597 


8660 


8723 


8786 


63 


690 


838849 


8912 


8975 


903S 


9101 


9164 


9227 


9289 


9352 


9415 


63 


691 


9478 


9541 


9604 


9667 


9729 


9792 


9855 


9918 


9981 


*oo43 


63 


692 


840106 


0169 


02S2 


0294 


0357 


0420 


0482 


0545 


060S 


0671 


63 


693 


0733 


0796 


0859 


0921 


0984 


1046 


1 109 


1172 


1234 


1297 


63 


694 


^359 


1422 


1485 


1547 


1610 


1672 


1735 


1797 


i860 


1922 


63 


695 


841985 


2047 


2II0 


2172 


2235 


2297 


2360 


2422 


2484 


2547 


62 


696 


2609 


2672 


2734 


2796 


2859 


2921 


2983 


3046 


3108 


3170 


62 


^^l 


3233 


3295 


3357 


3420 


3482 


3544 


3606 


3669 


3731 


3793 


62 


698 


3855 


391S 


39S0 


4042 


4104 


4166 


4229 


4291 


4353 


4415 


62 


699 


4477 


4539 


4601 


4664 


4726 


4788 


4850 


4912 


4974 


5036 


62 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




67 


7 


13 


20 


27 


34 


40 


47 


54 


60 


67 


0< 


66 


7 


13 


20 


26 


33 


40 


46 


53 


59 


66 




65 


7 


13 


20 


26 


33 


39 


46 


52 


59 


65 


d 

Oh 


^ 


6 


13 


19 


26 


32 


38 


45 


51 


58 


64 


63 


6 


13 


19 


25 


32 


38 


44 


50 


57 


63 


62 


6 


12 


19 


25 


31 


37 


43 


50 


56 


62 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



282 







TABLE VII— LOGARITHMS OF NUMBERS. 






1 

N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 
62 


700 


845098 


5160 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


701 


5718 


57S0 


5842 


5904 


5966 


6028 


6090 


6151 


6213 


6275 


62 


702 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 


6894 


62 


703 


6955 


7017 


7079 


7141 


7202 


7264 


7326 


7388 


7449 


7511 


62 


704 


7573 


7634 


7696 


7758 


78 19 


78S1 


7943 


8004 


8066 


8128 


62 


705 


848189 


8251 


8312 


S374 


S435 


8497 


8559 


8620 


86S2 


8743 


62 


706 


S805 


8866 


8928 


8989 


9051 


9112 


9174 


9235 


9297 


9358 


61 


707 


9419 


94S1 


9542 


9604 


9665 


9726 


978S 


9849 


991 1 


9972 


61 


708 


S50033 


0095 


0156 


0217 


0279 


0340 


0401 


0462 


0524 


05S5 


61 


709 


0646 


0707 


0769 


0830 


0891 


0952 


1014 


1075 


1136 


1 197 


61 


710 


851258 


1320 


I381 


1442 


1503 


1564 


1625 


1686 


1747 


1809 


61 


711 


1S70 


1931 


1992 


2053 


2114 


2175 


2236 


2297 


2358 


2419 


61 


712 


2480 


2541 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 


61 


713 


3090 


3150 


321I 


3272 


3333 


3394 


3455 


3516 


3577 


3637 


61 


714 


3698 


3759 


3S20 


3881 


3941 


4002 


4063 


4124 


4185 


4245 


6r 


715 


854306 


4367 


4428 


4488 


4549 


4610 


4670 


4731 


4792 


4852 


61 


716 


4913 


4974 


5034 


5095 


5156 


5216 


5277 


5337 


5398 


5459 


61 


717 


5519 


55S0 


5640 


5701 


5761 


5822 


5882 


5943 


6003 


6064 


6t 


718 


6124 


6185 


6245 


6306 


6^66 


6427 


6487 


6548 


6608 


6668 


60 


719 


6729 


67S9 


6S50 


6910 


6970 


7031 


7091 


7152 


7212 


7272 


60 


720 


857332 


7393 


7453 


7513 


7574 


7634 


7694 


7755 


7815 


7875 


60 


721 


7935 


7995 


8056 


8II6 


8176 


8236 


8297 


8357 


8417 


8477 


60 


722 


8537 


8597 


8657 


8718 


8778 


883S 


8898 


8958 


9018 


9078 


60 


723 


9138 


919S 


9258 


9318 


9379 


9439 


9499 


^9559 


9619 


9679 


60 


724 


9739 


9799 


9S59 


9918 


9978 


*oo3S 


♦0098 


*oi58 


*02l8 


*0278 


60 


725 


86033S 


0398 


0458 


0518 


0578 


0637 


0697 


0757 


0817 


0877 


60 


726 


0937 


0996 


1056 


1 1 16 


1176 


1236 


1295 


1355 


1415 


1475 


60 


727 


1534 


1594 


1654 


I7I4 


1773 


1S33 


1893 


1952 


2012 


2072 


60 


728 


2131 


2191 


2251 


2310 


2370 


2430 


24S9 


2549 


2608 


2668 


60 


729 


2728 


2787 


2S47 


2906 


2966 


3025 


3085 


3144 


3204 


3263 


60 


730 


863323 


3382 


3442 


3501 


3561 


3620 


3680 


3739 


3799 


3858 


59 


731 


3917 


3977 


4036 


4096 


4155 


4214 


4274 


4333 


4392 


4452 


59 


732 


451 1 


4570 


4630 


4689 


474S 


4808 


4867 


4926 


4985 


5045 


59 


733 


5104 


5163 


5222 


5282 


5341 


5400 


5459 


5519 


557S 


5637 


59 


734 


5696 


5755 


5814 


5S74 


5933 


5992 


6051 


61 10 


6169 


6228 


59 


735 


866287 


6346 


6405 


6465 


6524 


6583 


6642 


6701 


6760 


6819 


59 


736 


6S78 


6937 


6996 


7055 


7114 


7173 


7232 


7291 


7350 


7409 


59 


737 


7467 


7526 


7585 


7644 


7703 


7762 


7821 


7880 


7939 


7998 


59 


738 


8056 


8115 


8174 


8233 


8292 


8350 


8409 


8468 


8527 


8586 


59 


739 


8644 


8703 


8762 


8821 


8879 


8938 


8997 


9056 


9114 


9173 


59 


740 


869232 


9290 


9349 


9408 


9466 


9525 


9584 


9642 


9701 


9760 


59 


741 


9S18 


9877 


9935 


9994 


*oo53 


*oin 


♦0170 


*0228 


♦0287 


*o345 


59 


742 


870404 


0462 


0521 


0579 


0638 


0696 


0755 


0S13 


0S72 


0930 


5f 


743 


09S9 


1047 


1106 


1 164 


1223 


1281 


1339 


1398 


1456 


1515 


58 


744 


1573 


1631 


1690 


1748 


1806 


1S65 


1923 


198 1 


2040 


2098 


5f 


745 


872156 


2215 


2273 


2331 


2389 


2448 


2506 


2564 


2622 


2681 


58 


746 


2739 


2797 


2S55 


2913 


2972 


3030 


3088 


3146 


3204 


3262 


58 


747 


3321 


3379 


3437 


3495 


3553 


361 1 


3669 


3727 


37S5 


3844 


58 


748 


3902 


3960 


4018 


4076 


4134 


4192 


4250 


4308 


4366 


4424 


5^ 


749 


4482 


4540 


4598 


4656 


4714 


4772 


4830 


4888 


4945 


5003 


58 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


H 


62 


6 


12 


19 


25 


31 


37 


43 


50 


56 


62 


0, 


61 


6 


12 


18 


24 


31 


37 


43 


49 


55 


61 




60 


6 


12 


18 


24 


30 


36 


42 


48 


54 


60 


d 


59 


6 


12 


18 


24 


30 


35 


41 


47 


53 


59 


Oh 


58 


6 


12 


17 


23 


29 


35 


41 


46 


52 


58 




DiflF. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



283 







TABI.E VII —LOGARITHMS OF NUMBERS. 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Difi'. 


750 


875061 


5119 


5177 


5235 


5293 


5351 


5409 


5466 


5524 


5582 


58 


751 


5640 


5698 


5756 


5813 


5871 


5929 


5987 


6045 


6102 


6160 


58 


752 


6218 


6276 


6333 


6391 


6449 


6507 


6564 


6622 


6680 


6737 


58 


753 


6795 


6S53 


6910 


6968 


7026 


7083 


7141 


7199 


7256 


7314 


58 


754 


7371 


7429 


7487 


7544 


7602 


7659 


7717 


7774 


7832 


7889 


58 


755 


877947 


8004 


8062 


8119 


8177 


8234 


8292 


8349 


8407 


8464 


57 


756 


8522 


8579 


8637 


8694 


8752 


8809 


8866 


8924 


8981 


9039 


57 


757 


9096 


9'53 


92 1 1 


9268 


9325 


9383 


9440 


9497 


9555 


9612 


57 


758 


9669 


9726 


97S4 


9S41 


9898 


9956 


*ooi3 


*oo7o 


*0I27 


*oi85 


57 


759 


880242 


0299 


0356 


0413 


0471 


0528 


0585 


0642 


0699 


0756 


57 


760 


880814 


0871 0928 


0985 


1042 


1099 


1156 


1213 


I27I 


1328 


57 


761 


1385 


1442 1499 


1556 


1613 


1670 


1727 


1784 


I84I 


1898 


57 


762 


1955 


2012 2069 


2126 


2183 


2240 


2297 


2354 


24II 


2468 


57 


763 


2525 


2581 1 2638 


2695 


2752 


2809 


2866 


2923 


2980 


3037 


57 


764 


3093 


3150 3207 


3264 


3321 


3377 


3434 


3491 


3548 


3605 


57 


765 


883661 


3718 3775 


3832 


3888 


3945 


4002 


4059 


4II5 


4172 


57 


766 


4229 


4285 4342 


4399 


4455 


4512 


4569 


4625 


4682 


4739 


57 


767 


4795 


4852 1 4909 


4965 


5022 


5078 


5135 


5192 


5248 


5305 


57 


768 


5361 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


5813 


5870 


57 


769 


5926 


59S3 


6039 


6096 


6152 


6209 


6265 


6321 


6378 


6434 


56 


770 


886491 


6547 


6604 


6660 


6716 


6773 


6829 


6885 


6942 


6998 


56 


771 


7054 


7111 


7167 


7223 


7280 


7336 


7392 


7449 


7505 


7561 


56 


772 


7617 


7674 


7730 


7786 


7842 


7898 


7955 


801 1 


8067 


8123 


56 


773 


8179 


8236 


8292 


8348 


8404 


8460 


8516 


8573 


8629 


8685 


56 


774 


00^741 


8797 


8853 


8909 


8965 


9021 


9077 


9134 


9190 


9246 


56 


775 


889302 


9358 


9414 


9470 


9526 


9582 


9638 


9694 


9750 


9806 


56 


776 


9862 


9918 


9974 


*oo30 


*ooS6 


*oi4i 


*oi97 


*o253 


♦0309 


*0365 


56 


777 


890421 


0477 


0533 


0589 


0645 


0700 


0756 


0812 


0S6S 


0924 


56 


778 


09S0 


1035 


1091 


1 147 


1203 


1259 


1314 


1370 


1426 


1482 


56 


779 


1537 


1593 


1649 


1705 


1760 


1816 


1872 


1928 


1983 


2039 


56 


780 


892095 


2150 


2206 


2262 


2317 


2373 


2429 


2484 


2540 


2595 


56 


7?' 


2651 


2707 


2762 


2818 


2873 


2929 


2985 


3040 


3096 


3151 


56 


782 


3207 


3262 


3318 


3373 


3429 


34S4 


3540 


3595 


3651 


3706 


56 


783 


3762 


3817 


3873 


3928 


3984 


4039 


4094 


4150 


4205 


4261 


55 


784 


4316 


4371 


4427 


4482 


4538 


4593 


4648 


4704 


4759 


4814 


55 


7^5 


894S70 


4925 


4980 


5036 


5091 


5146 


5201 


5257 


5312 


5367 


55 


786 


5423 


5478 


5533 


5588 


5644 


5699 


5754 


5S09 


5864 


5920 


55 


7f7 


5975 


6030 


6085 


6140 


6195 


6251 


6306 


6361 


6416 


6471 


55 


788 


6526 


6581 


6636 


6692 


6747 


6S02 


6857 


6912 


6967 


7022 


55 


789 


7077 


7132 


71S7 


7242 


7297 


7352 


7407 


7462 


7517 


7572 


55 


790 


897627 


7682 


7737 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


55 


791 


8:76 


8231 


8286 


8341 


8396 


8451 


8506 


8561 


8615 


8670 


55 


792 


8725 


87S0 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 


55 


793 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9656 


9711 


9766 


55 


794 


9821 


9875 


9930 


9985 


*oo39 


*oo94 


*oi49 


*0203 


♦0258 


*03I2 


55 


795 


900367 


0422 


0476 


0531 


0586 


0640 


0695 


0749 


0S04 


0859 


55 


796 


0913 


0968 


1022 


1077 


1131 


1 186 


1240 


1295 


1349 


1404 


55 


797 


1458 


1513 


1567 


1622 


1676 


1731 


1785 


1840 


1894 


1948 


54 


798 


2003 


2057 


2112 


2166 


2221 


2275 


3329 


2384 


2438 


2492 


54 


799 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3036 


54 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




57 


6 


II 


17 


23 


29 


34 


40 


46 


51 


57 


0. 


56 


6 


II 


17 


22 


28 


34 


39 


45 


50 


56 


a. 


55 


6 


II 


17 


22 


28 


33 


39 


44 


50 


55 


54 


5 


II 


16 


22 


27 


32 


38 


43 


49 


54 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

1 



table; VII.— i^ogarithms of numbers. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


800 


903090 


3144 


3199 


3253 


3307 


3361 


3416 


3470 


3524 


3578 


54 


801 


3633 


3687 


3741 


3795 


3«49 


3904 


3958 


4012 


4066 


4120 


54 


802 


4174 


4229 


4283 


4337 


4391 


4445 


4499 


4553 


4607 


4661 


54 


803 


4716 


4770 


4824 


4878 


4932 


4986 


5040 


5094 


5148 


5202 


54 


804 


5256 


5310 


5364 


5418 


5472 


5526 


5580 


5634 


5688 


5742 


54 


805 


905796 


5850 


5904 


5958 


6012 


6066 


6119 


6173 


6227 


6281 


54 


806 


6335 


6389 


6443 


6497 


6551 


6604 


6658 


6712 


6766 


6820 


54 


807 


6S74 


6927 


6981 


7035 


7089 


7143 


7iq6 


7250 


7304 


7358 


54 


808 


7411 


7465 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 


54 


809 


7949 


8002 


8056 


8110 


8163 


8217 


8270 


8324 


8378 


8431 


54 


810 


908485 


8539 


8592 


8646 


8699 


8753 


8807 


8860 


8914 


8967 


54 


811 


9021 


9074 


9128 


9181 


9235 


9289 


9342 


9396 


9449 


9503 


54 


812 


9556 


9610 


9663 


9716 


9770 


9S23 


9877 


9930 


9984 


*0037 


53 


813 


910091 


0144 


0197 


0251 


0304 


0358 


041 1 


0464 


0518 


0571 


53 


814 


0624 


0678 


0731 


0784 


0838 


0891 


0944 


0998 


1051 


1 104 


53 


815 


911158 


1211 


1264 


1317 


1371 


1424 


1477 


1530 


1584 


1637 


53 


816 


1690 


1743 


3797 


1850 


1903 


1956 


2009 


2063 


2116 


2169 


53 


817 


2222 


2275 


2328 


2381 


2435 


2488 


2541 


2594 


2647 


2700 


53 


818 


2753 


2806 


2859 


2913 


2966 


3019 


3072 


3125 


3178 


3231 


53 


8ig 


3284 


3337 


3390 


3443 


3496 


3549 


3602 


3655 


3708 


3761 


53 


820 


913814 


3S67 


3920 


3973 


4026 


4079 


4132 


4184 


4237 


4290 


53 


821 


4343 


4396 


4449 


4502 


4555 


4608 


4660 


4713 


4766 


4819 


53 


822 


4872 


4925 


4977 


5030 


5083 


5136 


5189 


5241 


5294 


5347 


53 


823 


5400 


5453 


5505 


5558 


561 1 


5664 


5716 


5769 


5822 


5875 


53 


824 


5927 


5980 


6033 


6085 


6138 


6191 


6243 


6296 


6349 


6401 


53 


825 


916454 


6507 


6559 


6612 


6664 


6717 


6770 


6S22 


6875 


6927 


53 


826 


69S0 


7033 


7085 


7138 


7190 


7243 


7295 


7348 


7400 


7453 


53 


827 


7506 


7558 


761 1 


7663 


7716 


7768 


7820 


7873 


7925 


7978 


52 


828 


8030 


80S3 


8135 


8188 


8240 


8293 


8345 


8397 


8450 


8502 


52 


829 


8555 


8607 


8659 


8712 


8764 


8816 


8869 


8921 


8973 


9026 


52 


830 


919078 


9130 


9183 


9235 


9287 


9340 


9392 


9444 


9496 


9549 


52 


831 


9601 


9653 


9706 


9758 


9810 


9862 


9914 


9967 


*ooi9 


*oo7i 


52 


832 


920123 


0176 


0228 


0280 


0332 


0384 


0436 


0489 


0541 


0593 


52 


833 


0645 


0697 


0749 


0801 


0853 


0906 


0958 


lOIO 


1062 


1114 


52 


834 


1 166 


1218 


1270 


1322 


1374 


1426 


1478 


1530 


1582 


1634 


52 


835 


921686 


1738 


1790 


1842 


1894 


1946 


1998 


2050 


2102 


2154 


52 


836 


2206 


2258 


2310 


2362 


2414 


2466 


2518 


2570 


2622 


2674 


52 


837 


2725 


2777 


2829 


2881 


2933 


2985 


3037 


30S9 


3140 


3192 


52 


838 


3244 


3296 


3348 


3399 


3451 


3503 


3555 


3607 


3658 


3710 


52 


839 


3762 


3814 


3865 


3917 


3969 


4021 


4072 


4124 


4176 


4228 


52 


840 


924279 


4331 


4383 


4434 


4486 


4538 


4589 


4641 


4693 


4744 


52 


841 


4796 


4848 


4899 


4951 


5003 


5054 


5106 


5157 


5209 


5261 


52 


843 


5312 


5364 


5415 


5467 


5518 


5570 


5621 


5673 


5725 


5776 


52 


843 


5828 


5879 


5931 


5982 


6034 


6085 


6137 


6188 


6240 


6291 


51 


844 


6342 


6394 


6445 


6497 


6548 


6600 


6651 


6702 


6754 


6805 


51 


845 


926857 


6908 


6959 


701 1 


7062 


71 u 


7165 


7216 


7268 


7319 


51 


846 


7370 


7422 


7473 


7524 


7576 


7627 


7678 


7730 


7781 


7832 


51 


847 


7883 


7935 


7986 


8037 


8088 


8140 


8191 


8242 


8293 


8345 


51 


848 


8396 


8447 


8498 


8549 


8601 


8652 


8703 


8754 


8805 


8857 


51 


849 


8908 


8959 


9010 


9061 


9112 


9163 


9215 


9266 


9317 


9368 


51 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




55 


6 


II 


17 


22 


28 


33 


39 


44 


50 


55 


0, 


54 


5 


II 


16 


22 


27 


32 


38 


43 


49 


54 




53 


5 


II 


16 


21 


27 


32 


. 37 


42 


48 


53 




52 


5 


10 


16 


21 


26 


31 


36 


42 


47 


52 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



28s 



table; VII.— logarithms of numbers. 



1 

N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


850 


929419 


9470 


9521 


9572 


9623 


9674 


9725 


9776 


9827 


9879 


51 


851 


9930 


9981 


♦0032 


*oo83 


*oi34 


*oi85 


*0236 


*0287 


*0338 


♦0389 


51 


852 


930440 


0491 


0542 


0592 


0643 


0694 


0745 


0796 


0847 


0898 


51 


853 


0949 


1000 


1051 


1 102 


"53 


1204 


1254 


1305 


1356 


1407 


51 


854 


1458 


1509 


1560 


1610 


166 1 


1712 


1763 


1814 


1865 


1915 


51 


855 


931966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 


51 


856 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 


51 


857 


2981 


3031 


3082 


3133 


3183 


3234 


32S5 


3335 


3386 


3437 


51 


858 


3487 


3538 


3589 


3639 


3690 


3740 


3791 


3841 


3892 


3943 


51 


859 


3993 


4044 


4094 


4145 


4195 


4246 


4296 


4347 


4397 


4448 


51 


860 


934498 


4549 


4599 


4650 


4700 


4751 


4801 


4852 


4902 


4953 


50 


861 


5003 


5054 


5104 


5154 


5205 


5255 


5306 


5356 


5406 


5457 


50 


862 


5507 


5558 


5608 


5658 


5709 


5759 


5809 


5860 


5910 


5960 


50 


863 


601 1 


6061 


6111 


6162 


6212 


6262 


6313 


6363 


6413 


6463 


50 


864 


6514 


6564 


6614 


6665 


6715 


6765 


6815 


6865 


6916 


6966 


50 


865 


937016 


7066 


7117 


7167 


7217 


7267 


7317 


7367 


7418 


7468 


50 


866 


7518 


7568 


7618 


7668 


7718 


7769 


7819 


7869 


7919 


7969 


50 


867 


8019 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


50 


868 


8520 


8570 


8620 


8670 


S720 


8770 


8820 


8870 


8920 


8970 


50 


86g 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 


50 


870 


939519 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 


50 


871 


9400 I 8 


0068 


0118 


0168 


0218 


0267 


0317 


0367 


0417 


0467 


50 


872 


0516 


0566 


0616 


0666 


0716 


0765 


0815 


0865 


0915 


0964 


50 


873 


1014 


1064 


1114 


1163 


1213 


1263 


1313 


1362 


1412 


1462 


50 


874 


1511 


156 1 


161 1 


1660 


1710 


1760 


1809 


1859 


1909 


1958 


50 


^75 


942008 


2058 


2107 


2157 


2207 


2256 


2306 


2355 


2405 


2455 


50 


876 


2504 


2554 


2603 


2653 


2702 


2752 


2S01 


2851 


2901 


2950 


50 


877 


3000 


3049 


3099 


3148 


3198 


3247 


3297 


3346 


3396 


3445 


49 


878 


3495 


3544 


3593 


3643 


3692 


3742 


3791 


3841 


3890 


3939 


49 


879 


3989 


4038 


4088 


4137 


4186 


4236 


4285 


4335 


4384 


4433 


49 


880 


944483 


4532 


4581 


4631 


4680 


4729 


4779 


4828 


4S77 


4927 


49 


881 


4976 


5025 


5074 


5124 


5173 


5222 


5272 


5321 


5370 


5419 


49 


882 


5469 


5518 


5567 


5616 


5665 


5715 


5764 


5813 


5862 


5912 


49 


883 


5961 


6010 


6059 ! 6108 


6157 6207 


6256 


6305 


6354 


6403 


49 


11'^ 


6452 


6501 


6551 


6600 


6649 


6698 


6747 


6796 


6845 


6894 


49 


885 


946943 


6992 


7041 


7090 


7140 


71S9 


7238 


7287 


7336 


7385 


49 


886 


7434 


7483 


7532 


7581 


7630 


7679 


7728 


7777 


7826 


7875 


49 


887 


7924 


7973 


8022 


8070 


8119 


8168 


8217 


8266 


8315 


8364 


49 


888 


8413 


8462 


8511 


8560 


8609 


8657 


8706 


8755 


8804 


8853 


49 


889 


8902 


8951 


8999 


9048 


9097 


9146 


9195 


9244 


9292 


9341 


49 


890 


949390 


9439 


9488 


9536 


9585 


9634 


96S3 


9731 


97S0 


9829 


49 


891 


9878 


9926 


9975 


*0024 


*oo73 


*0I2I 


*oi70 


*02I9 


♦0267 


*03i6 


49 


892 


950365 


0414 


0462 


0511 


0560 


0608 


0657 


0706 


0754 


0803 


49 


893 


0851 


0900 


0949 


0997 


1046 


1095 


1143 


1192 


1240 


1289 


49 


894 


1338 


1386 


1435 


1483 


1532 


1580 


1629 


1677 


1726 


1775 


49 


895 


951823 


1872 


1920 


1969 


2017 


2066 


2114 


2163 


2211 


2260 


48 


896 


2308 


2356 


2405 


2453 


2502 


2550 


2599 


2647 


2696 


2744 


48 


IH 


2792 


2841 


2889 


2938 


2986 


3034 


3083 


3I3I 


3180 


3228 


48 


8g8 


3276 


3325 


3373 


3421 


3470 


3518 


3566 


3615 


3663 


3711 


48 


899 


3760 


3808 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194 


48 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


0. 


51 


5 


10 


15 


20 I 26 


31 


36 


41 


46 


51 


50 


5 


10 


15 


20 1 25 


30 


35 


40 


45 


50 




49 


5 


10 


15 


20 


25 


29 


34 


39 


44 


49 


48 


5 


10 


14 


19 


24 


29 


34 


38 


43 


48 




Diff. 


I 2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



286 







TABI,E VII.— LOGARITHMS OF NUMBERS. 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


900 


954243 


4291 


4339 


4387 


4435 


4484 


4532 


4580 


4628 


4677 


48 


901 


4725 


4773 


4821 


4869 


4918 


4966 


5014 


5062 


51 10 


5158 


48 


902 


5207 


5255 


5303 


5351 


5399 


5447 


5495 


5543 


5592 


5640 


48 


903 


5688 


5736 


5784 


5832 


5880 


5928 


5976 


6024 


6072 


6120 


48 


904 


6168 


6216 


6265 


6313 


6361 


6409 


6457 


6505 


6553 


6601 


48 


905 


956649 


6697 


6745 


6793 


6840 


68S8 


6936 


6984 


7032 


7080 


48 


906 


7128 


7176 


7224 


7272 


7320 


7368 


7416 


7464 


7512 


7559 


48 


907 


7607 


7655 


7703 


7751 


7799 


7847 


7894 


7942 


7990 


8038 


48 


908 


8086 


8134 


8181 


8229 


8277 


8325 


8373 


8421 


8468 


8516 


48 


909 


8564 


8612 


8659 


8707 


8755 


8803 


8850 


8898 


8946 


8994 


48 


910 


959041 


9089 


9137 


9185 


9232 


9280 


9328 


9375 


9423 


9471 


48 


911 


9518 


9566 


9614 


9661 


9709 


9757 


9804 


9852 


9900 


9947 


48 


912 


9995 


♦0042 


♦0090 


*oi38 


*oiS5 


*o233 


*02S0 


♦0328 


*o376 


*0423 


48 


913 


960471 


0518 


0566 


0613 


0661 


0709 


0756 


0804 


0851 


0899 


48 


914 


0946 


0994 


104 1 


10S9 


1 136 


1 184 


1231 


1279 


1326 


1374 


48 


915 


961421 


1469 


1516 


1563 


1611 


1658 


1706 


1753 


1801 


1848 


47 


916 


1895 


1943 


1990 


2038 


2085 


2132 


2180 


2227 


2275 


2322 


47 


917 


2369 


2417 


2464 


251 1 


2559 


2606 


2633 


2701 


2748 


2795 


47 


918 


2843 


2890 


2937 


2985 


3032 


3079 


3126 


3174 


3221 


3268 


47 


919 


3316 


3363 


3410 


3457 


3504 


3552 


3599 


3646 


3693 


3741 


47 


920 


963788 


3835 


3882 


3929 


3977 


4024 


4071 


4118 


4165 


4212 


47 


921 


4260 


4307 


4354 


4401 


4448 


4495 


4542 


4590 


4637 


4684 


47 


922 


4731 


4778 


4825 


4872 


4919 


4966 


5013 


5061 


5108 


5155 


47 


923 


5202 


5249 


5296 


5343 


5390 


5437 


5484 


5531 


5578 


5625 


47 


924 


5672 


5719 


5766 


5813 


5860 


5907 


5954 


6001 


6048 


6095 


47 


925 


966142 


6189 


6236 


6283 


6329 


6376 


6423 


6470 


6517 


6564 


47 


926 


6611 


6658 


6705 


6752 


6799 


6S45 


6892 


6939 


6986 


7033 


47 


927 


7080 


7127 


7173 


7220 


7267 


7314 


7361 


7408 


7454 


7501 


47 


928 


7548 


7595 


7642 


7688 


7735 


7782 


7829 


7875 


7922 


7969 


47 


929 


8016 


8062 


8109 


8156 


S203 


8249 


8296 


8343 


8390 


8436 


47 


930 


9684S3 


8530 


8576 


8623 


8670 


8716 


8763 


8810 


8856 


8903 


47 


931 


8950 


8996 


9043 


9090 


9136 


9183 


9229 


9276 


9323 


9369 


47 


932 


9416 


9463 


9509 


9556 


9602 


9649 


9695 


9742 


9789 


9835 


47 


933 


9882 


9928 


9975 


*002I 


*oo68 


*oii4 


*oi6i 


*0207 


*0254 


*0300 


47 


934 


970347 


0393 


0440 


0486 


0533 


0579 


0626 


0672 


0719 


0765 


46 


935 


970812 


0858 


0904 


0951 


0997 


1044 


1090 


1137 


1 183 


1229 


46 


935 


1276 


1322 


1369 


I4I5 


1461 


1508 


1554 


I60I 


1647 


1693 


46 


937 


1740 


1786 


1832 


1879 


1925 


197 1 


2018 


2064 


2110 


2157 


46 


938 


2203 


2249 


2295 


2342 


2388 


2434 


2481 


2527 


2573 


2619 


46 


939 


2666 


2712 


2758 


2804 


2851 


2S97 


2943 


29S9 


3035 


3082 


46 


940 


973128 


3174 


3220 


3266 


3313 


3359 


3405 


3451 


3497 


3543 


46 


941 


3590 


3636 


3682 


3728 


3774 


3820 


3866 


3913 


3959 


4005 


46 


942 


4051 


4097 


4143 


4189 


4235 


4281 


43^7 


4374 


4420 


4466 


46 


943 


4512 


4558 


4604 


4650 


4696 


4742 


4788 


4834 


48S0 


4926 


46 


944 


4972 


5018 


5064 


5IIO 


5156 


5202 


5248 


5294 


5340 


5386 


46 


945 


975432 


5478 


5524 


5570 


5616 


5662 


5707 


5753 


5799 


5845 


46 


946 


5891 


5937 


5983 


6029 


6075 


6121 


6167 


6212 


6258 


6304 


46 


947 


6350 


6396 


6442 


6488 


6533 


6579 


6625 


6671 


6717 


6763 


46 


948 


6808 


6854 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 


46 


949 


7266 


7312 


7358 


7403 


7449 


7495 


7541 


75S6 


7632 


7678 


46 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




49 


5 


10 


15 


20 


25 


29 


34 


39 


44 


0. 


48 


5 


10 


14 


19 


24 


29 


34 


38 


43 


48 


• 


^l 


5 


9 


14 


19 


24 


28 


33 


38 


42 


47 


0. 


46 


5 


9 


14 


18 


23 


28 


32 


37 


41 


46 




DiflF. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



287 



TABIvB VII.— LOGARITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


950 


977724 


7769 


7815 


7861 


7906 


7952 


7998 


8043 


8089 


8135 


46 


951 


81S1 


8226 


8272 


8317 


8363 


8409 


8454 


8500 


8546 


8591 


46 


952 


8637 


8683 


8728 


8774 


8819 


8S65 


891 1 


8956 


9002 


9047 


46 


953 


9093 


9138 


9184 


9230 


9275 


9321 


9366 


9412 


9457 


9503 


46 


954 


9548 


9594 


9639 


9685 


9730 


9776 


9821 


9867 


9912 


9958 


46 


955 


980003 


0049 


0094 


0140 


0185 


0231 


0276 


0322 


0367 


0412 


45 


956 


0458 


0503 


0549 


0594 


0640 


0685 


0730 


0776 


0821 


0867 


45 


957 


0912 


0957 


1003 


1048 


1093 


"39 


1 184 


1229 


1275 


1320 


45 


958 


1366 


1411 


1456 


1 501 


1547 


1592 


1637 


1683 


1728 


1773 


45 


959 


1819 


1864 


1909 


1954 


2000 


2045 


2090 


2135 


2181 


2226 


45 


960 


982271 


2316 


2362 


2407 


2452 


2497 


2543 


2588 


2633 


2678 


45 


g6i 


2723 


2769 


2814 


2859 


2904 


2949 


2994 


3040 


3085 


3130 


45 


962 


3175 


3220 


3265 


3310 


3356 


3401 


3446 


3491 


3536 


3581 


45 


963 


3626 


3671 


3716 


3762 


3807 


3852 


3897 


3942 


3987 


4032 


45 


964 


4077 


4122 


4167 


4212 


4257 


4302 


4347 


4392 


4437 


44S2 


45 


965 


984527 


4572 


4617 


4662 


4707 


4752 


4797 


4842 


48S7 


4932 


45 


966 


4977 


5022 


5067 


5112 


5157 


5202 


5247 


5292 


5337 


5382 


45 


967 


5426 


5471 


5516 


5561 


5606 


5651 


5696 


5741 


5786 


5830 


45 


968 


5875 


5920 


5965 


6010 


6055 


6100 


6144 


6189 


6234 


6279 


45 


969 


6324 


6369 


6413 


6458 


6503 


6548 


6593 


6637 


6682 


6727 


45 


970 


986772 


6817 


6861 


6906 


6951 


6996 


7040 


7085 


7130 


7175 


45 


971 


7219 


7264 


7309 


7353 


7398 


7443 


7488 


7532 


7577 


7622 


45 


972 


7666 


7711 


7756 


7800 


7845 


7890 


7934 


7979 


8024 


8068 


45 


973 


8113 


8157 


8202 


8247 


8291 


8336 


83S1 


8425 


8470 


8514 


45 


974 


8559 


S604 


S648 


8693 


8737 


8782 


8826 


8871 


8916 


8960 


45 


975 


989005 


9049 


9094 


9138 


9183 


9227 


9272 


9316 


9361 


9405 


45 


976 


9450 


9494 


9539 


9583 


9628 


9672 


9717 


9761 


9806 


9850 


44 


977 


9S95 


9939 


9983 


*0028 


*0072 


*oii7 


*oi6i 


*0206 


*025O 


*0294 


44 


978 


990339 


0383 


0428 


0472 


0516 


0561 


0605 


0650 


0694 


0738 


44 


979 


0783 


0S27 


0871 


0916 


0960 


1004 


1049 


1093 


U37 


1182 


44 


980 


991226 


1270 


1315 


1359 


1403' 


1448 


1492 


1536 


1580 


1625 


44 


g8i 


1669 


1713 


1758 


1802 


1846 


1890 


1935 


1979 


2023 


2067 


44 


982 


2111 


2156 


2200 


2244 


2288 


2333 


2377 


2421 


2465 


2509 


44 


983 


2554 


2598 


2642 


26S6 


2730 


2774 


28 19 


2863 


2907 


2951 


44 


984 


2995 


3039 


3083 


3127 


3172 


3216 


3260 


3304 


3348 


3392 


44 


9ol 


993436 


34S0 


3524 


3568 


3613 


3657 


3701 


3745 


37S9 


3833 


44 


986 


3877 


3921 


3965 


4009 


4053 


4097 


4141 


4185 


4229 


4273 


44 


987 


4317 


4361 


4405 


4449 


4493 


4537 


45S1 


4625 


4669 


4713 


44 


988 


4757 


4801 


4845 


4889 


4933 


4977 


5021 


5065 


5108 


5152 


44 


989 


5196 


5240 


5284 


5328 


5372 


5416 


5460 


5504 


5547 


5591 


44 


990 


995635 


5679 


5723 


5767 


581 1 


5854 


5898 


5942 


5986 


6030 


44 


991 


6074 


6117 


6161 


6205 


6249 


6293 


6337 


6380 


6424 


6468 


44 


992 


6512 


6555 


6599 


6643 


6687 


6731 


6774 


6818 


6S62 


6906 


44 


993 


6949 


6993 


7037 


7080 


7124 


716S 


7212 


7255 


7299 


7343 


44 


994 


73S6 


7430 


7474 


7517 


7561 


7605 


7648 


7692 


7736 


7779 


44 


995 


997823 


7867 


7910 


7954 


7998 


8041 


8085 


8129 


8172 


8216 


44 


996 


8259 


8303 


8347 


8390 


8434 


8477 


8521 


8564 


8608 


8652 


44 


997 


8695 


8739 


8782 


8826 


8S69 


8913 


8956 


9000 


9043 


9087 


44 


998 


9131 


9174 


9218 


9261 


9305 


9348 


9392 


9435 


9479 


9522 


44 


999 


9565 


9609 


9652 


9696 


9739 


9783 


9S26 


9870 


9913 


9957 


43 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




46 


5 


9 


14 


18 


23 


28 


32 


37 


41 


46 


a. 


45 


5 


9 


14 18 


23 


27 


32 


36 


41 


45 


0. 


44 


4 


9 


13 18 


22 


26 


31 


35 


40 


44 


43 


4 


9 


13 17 


22 


26 


30 


34 


39 


43 
Diff. 




Diff. 


I 


• 2 


3 4 


5 


6 


7 


8 


9 



288 



TABIvS VII.— LOGA.RITHMS OF NUMBERS. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


1 

lOOO 


000000 


0043 


0087 


0130 


0174 


0217 


0260 


0304 


0347 


0391 


43 


lOOI 


0434 


0477 


0521 


0564 


0608 


0651 


0694 


0738 


0781 


0S24 


43 


I002 


0S6S 


0911 


0954 


0998 


104 1 


1084 


112S 


1171 


1214 


1258 


43 


1003 


1301 


1344 


1388 


1431 


1474 


1517 


1561 


1604 


1647 


1690 


43 


1004 


1734 


1777 


1820 


1863 


1907 


1950 


1993 


2036 


2080 


2123 


43 


1005 


002166 


2209 


2252 


2296 


2339 


2382 


2425 


2468 


2512 


2555 


43 


1006 


2598 


2641 


2684 


2727 


2771 


2814 


2857 


2900 


2943 


2986 


43 


1007 


3029 


3073 


3116 


3159 


3202 


3245 


3288 


3331 


3374 


3417 


43 


1008 


3461 


3504 


3547 


3590 


3633 


3676 


3719 


3762 


3805 


3848 


43 


ICX39 


3891 


3934 


3977 


4020 


4063 


4106 


4149 


4192 


4235 


4278 


43 


lOIO 


004321 


4364 


4407 


4450 


4493 


4536 


4579 


4622 


4665 


4708 


43 


lOII 


4751 


4794 


4837 


4880 


4923 


4966 


5009 


5052 


5095 


5138 


43 


I0I2 


5181 


5223 


5266 


5309 


5352 


5395 


5438 


5481 


5524 


5567 


43 


1013 


5609 


5652 


5695 


5738 


5781 


5824 


5867 


5909 


5952 


5995 


43 


IOI4 


6038 


60S I 


6124 


6166 


6209 


6252 


6295 


6338 


6380 


6423 


43 


IOI5 


006466 


6509 


6552 


6594 


6637 


6680 


6723 


6765 


6808 


6851 


43 


IO16 


6894 


6936 


6979 


7022 


7065 


7107 


7150 


7193 


7236 


7278 


43 


JOI7 


7321 


7364 


7406 


7449 


7492 


7534 


7577 


7620 


7662 


7705 


43 


1018 


7748 


7790 


7833 


7876 


7918 


7961 


8004 


8046 


80S9 


8132 


43 


loig 


8174 


8217 


8259 


8302 


8345 


8387 


8430 


8472 


8515 


8558 


43 


1020 


008600 


8643 


8685 


8728 


8770 


8813 


8856 


8898 


8941 


8983 


43 


102 1 


9026 


9068 


9111 


9153 


9196 


9238 


9281 


9323 


9366 


9408 


42 


1022 


9451 


9493 


9536 


9578 


9621 


9663 


9706 


9748 


9791 


9833 


42 


1023 


9876 


9918 


9961 


*ooo3 


*0045 


*oo88 


*oi30 


*oi73 


*02I5 


♦0258 


42 


1024 


010300 


0342 


0385 


0427 


0470 


0512 


0554 


0597 


0639 


0681 


42 


X025 


010724 


0766 


0809 


0851 


0S93 


0936 


0978 


1020 


1063 


1 105 


42 


1026 


1 147 


1 190 


1232 


1274 


1317 


1359 


1401 


1444 


i486 


1528 


42 


1027 


1570 


1613 


1655 


1697 


1740 


1782 


1824 


1866 


1909 


1951 


42 


1028 


1993 


2035 


2078 


2120 


2162 


2204 


2247 


2289 


2331 


2373 


42 


xo2g 


2415 


2458 


2500 


2542 


25S4 


2626 


2669 


2711 


2753 


2795 


42 


1030 


012837 


2879 


2922 


2964 


3006 


3048 


3090 


3132 


3174 


3217 


42 


1031 


3259 


3301 


3343 


33S5 


3427 


3469 


35" 


3553 


3596 


3638 


42 


1032 


3680 


3722 


3764 


3806 


3848 


3890 


3932 


3974 


4016 


4058 


42 


1033 


4100 


4142 


4184 


4226 


4268 


4310 


4353 


4395 


4437 


4479 


42 


1034 


4521 


4563 


4605 


4647 


4689 


4730 


4772 


4814 


4856 


4898 


42 


1035 


014940 


4982 


5024 


5066 


5108 


5150 


5192 


5234 


5276 


5318 


42 


1036 


5360 


5402 


5444 


5485 


5527 


5569 


561 1 


5653 


5695 


5737 


42 


1037 


5779 


5821 


5863 


5904 


5946 


59S8 


6030 


6072 


6114 


6156 


42 


1038 


6197 


6239 


6281 


6323 


6365 


6407 


6448 


6490 


6532 


6574 


42 


1039 


6616 


6657 


6699 


6741 


6783 


6824 


6866 


6908 


6950 


6992 


42 


1040 


017033 


7075 


7117 


7159 


7200 


7242 


7284 


7326 


7367 


7409 


42 


1041 


7451 


7492 


7534 


7576 


7618 


7659 


7701 


7743 


7784 


7826 


42 


1042 


7868 


7909 


7951 


7993 


8034 


8076 


8118 


8159 


8201 


8243 


42 


1043 


8284 


8326 


836S 


8409 


8451 


8492 


8534 


8576 


8617 


8659 


42 


1044 


8700 


8742 


87S4 


8825 


8867 


8908 


8950 


8992 


9033 


9075 


42 


1045 


019116 


9158 


9199 


9241 


9282 


9324 


9366 


9407 


9449 


9490 


42 


1046 


9532 


9573 


9615 


9656 


9698 


9739 


9781 


9822 


9864 


9905 


41 


1047 


9947 


998S 


*oo30 


♦0071 


*oii3 


*oi54 


*oi95 


*0237 


♦0278 


*0320 


41 


1048 


020361 


0403 


0444 


04 86 


0527 


0568 


0610 


0651 


0693 


0734 


41 


1049 


0775 


0817 


0858 


0900 


0941 


0982 


1024 


1065 


1 107 


1148 


41 


1050 


021 1S9 


1231 


1272 


1313 


1355 


1396 


1437 


1479 


1520 


I56I 


41 


N. 


Diff. 


I 


2 

9 


3 


4 


5 


6 


7 


8 


9 


Diff. 


. 
OT 
H 


44 


4 


13 


18 


22 


26 


31 


35 


40 


44 


43 


4 


9 


13 


17 


22 


26 


30 


34 


39 


43 




42 


4 


8 


13 


17 


21 


25 


29 


34 


38 


42 


41 


4 


8 


12 


16 


21 


25 


29 


33 


37 


41 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



289 



INDEX 



Article Page 

Accessibility of standing timber, definition of 175 178 

Account, general outlay and income, in forestry 131 118 

profit and loss, in forestry 131 118 

trading and profit and loss, in forestry 131 118 

Accounts, capital 20 11 

capital, in forestry 131 118 

cost 25 16 

cost, in forestry 92 70 

economic, forms of, in forestry 132 1 19 

outlay and income 21 12 

profit and loss 21 12 

proprietary 19 1 1 

proprietary, in forestry 91 69 

specific 19 II 

specific, in forestry, forms for 131 117 

valuation 54 35 

valuation, versus specific accounts 19 11 

valuation, in forestry 110 85 

Accumulations of compound interest, effect of rate of interest upon. . . 51 30 

Additions to capital 73 49 

Administration expenses 100 75 

iEsthetic values 147 138 

Age, economic 145 137 

Agricultural land, expectation value of 237 230 

sale value of 238 230 

soils, definition of 225 226 

value, timber as an 239 230 

versus forest values of land 236 229 

Agriculture versus forestry as a source of livelihood 232 227 

All-aged stand, taxes paid upon 158 148 

Amortization, definition of 173 173 

Annual profits 40 23 

Anticipation of continuous profits 126 107 

Anticipated profits on young timber 124 106 

Application of methods of computing depreciation in lumbering 178 185 

Appraisal in lumbering 120 102 

of damages, principles underlying 133 1 20 

timber left after logging 107 S3 

value 60 38 

291 



292 INDEX 

Article Page 

Appraisals, field 213 216 

of stumpage, price basis in 172 170 

value 171 169 

stumpage, reports 224 222 

stumpage, increasing future values as basis of 196 206 

principle underlying 18 10 

Appraised value 17 10 

effect of capital value upon 70 45 

Assets, appreciation of 73 50 

in balance sheet 73 46 

re- valuation of 73 48 

valuation accounts for 19 11 

Average logging costs, the basis of stumpage appraisals 175 179 

Balance sheet 73 48 

economic, in forestry 132 119 

in forestry 131 117 

problem of the 73 46 

specific, in forestry 120 100 

Bark-boring beetles 202 211 

Basis for profits in lumbering, investment 178 184 

of comparison of agricultural with forest values of land 236 229 

damages, expectation or capital value *..... 139 129 

sale value 138 128 

stumpage appraisals, increasing future values as 195 206 

value of forests, income as Ill 85 

Bonds, timber, interest on, as a carrying charge 181 192 

on standing timber 96 72 

Boxes and crates, use of wood for 189 199 

Brown-tail moth 202 2 1 1 

Brush burning, cost of 100 74 

Building, use of wood for 189 199 

Business investments, rate of interest for 47 28 

of forest production, the 90 68 

venture 28 17 

Cancellation of classification of lands for forest taxation 166 164 

of cost of land from sale of timber 107 83 

Capital 12 6 

additions to 73 49 

deductions from 73 49 

definition of 12 7 

working 24 15 

account, nature of 20 12 

accounts 20 11 

in forestry 131 118 

and income, distinction in timber property 156 145 

expenditures, in forestry 93 71 



INDEX 293 

Article Page 

Capital, invested in forest production, earning power of 129 11 1 

investment, stumpage as a 176 180 

returns on 31 18 

stock 28 17 

value, a basis of damages 139 1 29 

definition of 62 39 

effect of rate of interest on 66 42 

effect upon appraised value 70 45 

sale value 69 44 

independence of past outlay or cost 68 44 

of forest soil 116 92 

future sums 77 54 

perpetual rentals 86 62 

temporary annual rentals 81 58 

intermittent rentals 83 60 

time element in 65 42 

uncertainty of 67 43 

values, inflation of 71 45 

Capitalist, function of the '. 13 7 

Capitalization, regulation of 72 46 

Capitalized expenses, as additions to capital 73 50 

income value, definition of 62 40 

rental value, definition of 62 40 

value, definition of 62 39 

Carrying charge, interest as a 36 22 

charges versus profits on stumpage 181 191 

Chestnut bark disease 203 211 

Classification of costs in forest production 104 76 

land 235 229 

land, national forest poHcy in 166 164 

lands, cancellation of, in forest taxation 250 238 

Clear lumber 184 196 

Cleared land versus stump land 240 231 

Clearing stump lands, cost of 241 232 

Climate, agricultural 228 226 

Climatic injuries as a physical risk 204 211 

Closeness of utilization 186 197 

as affecting timber estimates 217 219 

Combined capital tax and income tax 163 154 

Commutation tax on forest property, Massachusetts 166 163 

Comparison of agricultural and forest values of land 236 229 

agriculture with forestry as a source of livelihood 232 227 

bare forest soil with agricultural soil 248 237 

costs, profits and stumpage value by overturn methods, diagram III 177 184 

results of simple and compound interest 49 28 

taxes on different forests. Table II 158 148 

forest rent versus soil rent 161 151 

total forest values with value of agricultural soil 249 237 



294 INDEX 

Article Page 

Compensation, in danaages 133 120 

Competition, effect of 7 4 

Compound interest, definition of 16 8 

comparison of results with simple interest 49 28 

uses of 16 9 

Computation of taxes under general property tax 164 157 

Connecticut, taxation of forests in 166 161 

Constitutional provisions of general property tax 166 165 

Continuous forest production, profits from 125 107 

value of forest property for 113 88 

profits, anticipation of 126 107 

Contractors' profits in logging 177 182 

Contracts, long term, revision of stumpage values in 196 207 

to provide against damages 140 132 

Control of risks, insurance 209 213 

private measures 211 214 

public measures 210 213 

Conversion of intermittent into annual rentals 88 65 

Correction factor in timber estimating 222 221 

Cost accounts 25 16 

in forestry 92 70 

and value, essential difference between 58 37 

as a basis of value 56 35 

interest as a 36 20 

of assets, addition of annual deficit to 73 48 

brush burning 100 74 

clearing stump lands 241 232 

growing timber, calculation of 105 77 

investments in standing timber 106 79 

labor, in lumbering 190 201 

many-aged forests 108 83 

milling 174 177 

producing a normal forest , 109 84 

raw material, stumpage as a 176 i8r 

re-estabhshing protective cover, as basis of damages 146 138 

replacement, as basis of damages 137 1 26 

restoration, in damages 133 121 

slash disposal 100 74 

transportation, elements in 98 73 

past. Independence of capital value and 68 44 

Costs, formulae for 243 

future, effect on value 10 5 

of forestry compared with destructive lumbering 107 81 

logging 175 178 

in forest production, classification of 104 76 

specific 25 16 

Cruisers, timber 218 219 

Current annual forest per cent 129 114 



INDEX 295 

Article Page 

Damage by fire, character of 135 122 

to forest soil 143 135 

forest property, elements of 133 122 

immature timber, partial loss 141 132 

total loss 142 133 

many-aged stands 145 137 

merchantable timber 140 131 

single trees 144 136 

soil, expressed in extra initial costs 142 134 

watersheds 146 137 

Damages, basis of; cost of replacement 137 126 

expectation or capital value, a basis of 139 129 

formulas for 247 

increased future prices not a basis of 139 130 

principles underlying appraisal of 133 1 20 

punitive 147 139 

rate of interest as affecting 139 131 

sale value a basis of 138 1 28 

Deductions from capital 73 49 

Deferred profits 41 23 

Definition of symbols 241 

Defohating insects 202 211 

Demand 5 2 

Depreciation as a cost of milling 174 177 

a deduction from capital 73 49 

an expense in logging 175 179 

definition of 173 173 

formulae for 247 

fund 173 173 

Hunter's formula 173 175 

methods of reckoning 173 1 74 

necessity for, in accounting 20 11 

Destructive lumbering, costs of, compared with forestry 107 81 

profits in 122 105 

value of forest property for 112 86 

Deterioration of merchantable timber, damages due to 140 132 

standing timber 185 196 

Determination of legitimate profits in lumbering 177 181 

Diagram I, periods required for $1 to multiply 51 31 

II, method of balancing future costs and income 115 93 

III, comparison of stumpage values, by overturn methods 177 184 

Diaporthe parasitica 203 211 

Difference between cost and value, essential 58 37 

Discount 15 8 

factor, definition of 74 53 

Discrimination against forest values in land classification 246 236 

in favor of forest values in land classification 247 236 

Diseases, fungous 203 211 



296 INDEX 

Article Page 

Disposition of income 30 17 

Distinction between capital and income in timber property 156 145 

Dividends, interest versus 32 18 

Douglas fir, deterioration of, in Washington State 185 196 

Doyle log rule 179 187 

Doyle-Scribner log rule 179 187 

Earning power of capital invested in forest production 129 in 

an investment 121 105 

Economic accounts, forms of, in forestry 132 119 

age of a stand 145 137 

balance sheet, in forestry 132 1 19 

comparison, in accounting 73 52 

factors, in classification of soil as agricultural 231 227 

forecast, in forestry 120 loi 

opportunity 27 16 

per cent earned on forest investments 129 112 

profits 120 104 

Effect of capital value upon appraised value 70 45 

sale value 69 44 

deferred income upon rate of interest 48 28 

general property tax on forest production •. . . 166 158 

present condition of forest upon choice of methods of taxation. . . . 158 147 

rate of interest upon accumulations of compound interest 51 30 

interest upon capital value 66 42 

risks on the business of forest production 212 214 

substitutes on wood prices 189 198 

taxes on property values 153 143 

Effort or outlay 6 3 

Elements of damage to forest property 134 122 

value for forest land 243 233 

Enterpriser, definition of term 39 23 

Enterpriser's profit or gain 39 23 

Entrepreneur, definition of term 39 23 

Equahty of taxation 153 143 

Errors in methods of timber estimating 219 220 

Estimation of standing timber 215 218 

Even-aged forest, value for any year 115 90 

for any year, formula 116 95 

just previous to cutting 114 89 

stand, taxes paid upon 158 148 

Exchange 29 17 

Expectation value, a basis of damages 139 129 

definition of 62 39 

of agricultural soil 237 230 

forest soil 116 92 

future series 77 54 

perpetual rentals 86 62 



INDEX 297 

Article Page 

Expectation value, of temporary annual rentals 81 58 

intermittent rentals 83 60 

Expenses, future, appraisal of 64 41 

included in outlay and income accounts 21 12 

investments versus 22 13 

or temporary outlay in forestry 94 71 

versus value 57 35 

Exploitation of land purchasers 234 229 

Factors affecting future value of forest products 182 195 

determining stumpage prices 170 167 

Federal income tax law, with reference to cost accounts for parcels of 

land 181 193 

Field appraisals, scope of 213 216 

methods of timber estimating 218 219 

Final income, definition of 61 38 

Financial risks 208 212 

definition of 198 208 

Finished products, prices of 8 4 

Fire as a moral risk 207 212 

physical risk 200 209 

killed timber, damages for 140 131 

hnes, cost of 100 75 

public measures for control of 210 213 

Fire-resistance in trees 200 209 

Forced sales 17 10 

Forecast, economic, in forestry 120 loi 

or prospectus, in accounting 73 51 

Forest of 50 acres, taxes paid upon 158 148 

investments, rate of interest on 52 32 

land bare of timber, taxation of 166 161 

tax 160 150 

per cent, current annual 129 114 

mean annual 129 114 

production, classification of costs in 104 76 

continuous, profits from 125 107 

value of forest property for 113 88 

earning power of capital invested in 129 in 

effect of general property tax upon 165 158 

risks upon 212 214 

versus lumbering 90 68 

products, changes in prices of 188 197 

future value of 182 195 

property, elements of damage to 134 122 

sale value of 245 235 

tax 159 149 

tax reform for 166 160 

value, for destructive lumbering 112 86 



298 INDEX 

' Article Page 

Forest rent, theory of 156 146 

versus soil rent, comparison of taxes on 161 151 

soil, damage to 143 135 

value of 116 92 

young timber as part of value of 244 234 

Forest statics, definition of 120 100 

taxation in Connecticut 166 161 

Massachusetts 166 161 

Pennsylvania 166 161 

problem of interest in 157 146 

valuation, summary of formulae in 243 

values, discrimination against, in land classification 246 236 

in favor of, in land classification 247 236 

utilization, business of 90 68 

versus agricultural values of land 236 229 

Forestry, interest rates in, compared with other investments 53 33 

versus agriculture as a source of livelihood 232 227 

Forms for specific accounts in forestry 131 117 

economic accounts in forestry 132 119 

Formulae for costs 243 

damages 247 

depreciation 247 

geometric series 248 

geometric series, discussion of 80 57 

interest earned 246 

profits 246 

stumpage values 248 

values 244 

in forest valuation, summary 243 

of compound interest, summary 240 

Fumes, as a physical risk 205 212 

Fungous diseases, as a physical risk 203 211 

Future crops of trees, as a measure of damage to soil 143 135 

expenses, appraisal of 64 41 

in taxation 162 152 

income as a basis of value 61 38 

operating costs, effect on stumpage values 190 201 

prices and values, uncertainty of 63 41 

as a basis of damages 139 130 

supply of timber, as a local factor in stumpage appraisals 193 204 

transportation facilities, in stumpage appraisals 191 202 

value of forest products 182 195 

temporary annual rentals 79 56 

intermittent rentals 82 59 

or cost of single sums 76 53 

values, increasing, as basis of stumpage appraisals 195 206 



INDEX 299 

Article Page 

Gauging of risks 199 209 

General outlay and income account in forestry 131 118 

price changes as affecting stumpage values 187 196 

property tax, the 154 144 

effect of, upon forest production 165 158 

on forest property 164 155 

Geometric series, formulae for 248 

formulas for, discussion of 80 57 

Grades of lumber, prices for, as basis of stumpage appraisals 172 171 

Grading logs 223 222 

Grass, inflammability 200 2 10 

Growing stock, even-aged, value of 119 98 

many-aged, value of 119 99 

Growth in volume of stand 183 195 

Gypsy moth 202 211 

Hardwood litter, inflammability 200 2 10 

Hazard, in risks, definition of 199 209 

Humus or duff, inflammability 200 210 

Hunter 's formula for depreciation and interest 173 1 76 

Immature timber, partial loss, damages 141 132 

total loss, damages 142 133 

Improvement in quality of products : 184 196 

Improvements, permanent investment in 96 73 

Income 26 16 

accounts, outlay and 21 12 

as the basis of value of forests Ill 85 

disposition of 30 17 

future, as a basis of value 61 38 

interest as 37 22 

or products tax 162 152 

potential 73 48 

secondary, from forests Ill 86 

tax, combined with capital tax 163 154 

law, federal, with relation to cost accounts by parcels 181 193 

on 150 141 

timber lands 162 152 

value, capitalized, definition of 62 40 

definition of 62 40 

versus profits 42 24 

Increase in stumpage value, rate of 194 204 

Increased future prices not a basis of damages 139 130 

Increasing future values as basis of stumpage appraisals 195 206 

Independence of capital value and past outlay or cost 68 44 

Industries and markets, local, effect on stumpage appraisals 192 203 

Inflation of capital values 71 45 

Influence of personality on the rate of interest 44 26 



300 INDEX 

Article Page 

Influences determining the rate of interest 43 26 

Injurious fumes, as a physical risk 205 212 

Insects, as a physical risk 202 211 

Installation, period of, in business 23 14 

Insurance on timber 209 213 

Intention to grow timber, influence in appraising damages to young 

timber 138 1 29 

Interest 14 7 

as a cost 36 20 

as distinguishing income from enterprisers' profits 42 25 

as income 37 22 

cannot be deducted from income; federal income tax 162 153 

charges, as an expense 103 76 

compound 16 8 

definition of 14 8 

earned, formulte for 246 

not a cost in determining legitimate profit in lumbering 178 185 

on bonds, as a carr>ang charge 181 192 

problem of, the 36 20 

in forest taxation 157 146 

rate of, the 38 22 

rate of, for business investments 47 28 

rates in forestry, comparison with other investments 53 ^^ 

rates paid by savings banks 53 t,^ 

simple 16 9 

versus dividends 32 18 

versus value 57 35 

Inventory, definition of 55 35 

Investments, business, rate of interest in 47 28 

forest, rate of interest in 52 32 

in lumbering, status of, resembling forest production 120 103 

or permanent outlay in forestry 93 71 

other than forestry, comparison of interest rates with forestry 53 33 

versus expenses 22 13 

Investment basis for profits in lumbering 178 184 

in standing timber, total cost of 106 79 

seed trees 107 82 

total 24 14 

Irregular income, value of many-aged forests producing 118 97 

Labor, cost of, in lumbering 190 201 

Land, agricultural versus forest values of 236 229 

classification 236 229 

national forest policy in 250 238 

investment in 96 71 

prices for 9 5 

purchasers, exploitation of 234 229 

tax, forest 160 150 



INDEX 301 

Article Page 

Landscape gardening as basis for appraising damages 147 139 

Larch sawfly 202 211 

Legitimate profits in lumbering — overturn method 177 181 

versus speculative value 67 43 

Liabilities, in balance sheet 73 46 

Liability, in risks, definition of 199 209 

Life insurance, interest rates in 53 ^^ 

Limitation of opportunity 50 29 

Loans 14 8 

Local factors in stumpage appraisals; industries and markets 192 203 

stumpage appraisals; future supply of timber 193 204 

stumpage appraisals; future transportation facilities 191 202 

revenue, maintenance of, in forest taxation 166 i6r 

Logarithms, use of 78 55 

Log grades 223 222 

markets 172 1 70 

rules 216 218 

Logging, definition of 90 68 

Logging chance, definition of 213 216 

costs and profit 175 178 

effect on fire hazard 200 2 10 

Logs, price of, as basis of stumpage appraisal 172 170 

Long term contracts, revision of stumpage values in 196 207 

Loss in value of entire property, a basis of damages 138 128 

of income in damages 133 121 

Lumbering, destructive, costs of, compared with forestry 107 81 

status of investment in, resembling forest production 120 103 

versus forest production 90 68 

Maintenance of local revenue, in forest taxation 166 161 

Many-aged forests, cost of 108 83 

producing irregular income, value of 118 97 

regular income, value of 117 96 

stands, damage to 145 137 

Map, reconnaissance 214 217 

Marketing of wind-thrown timber 201 211 

Alarkets, local, effect on stumpage appraisals 192 203 

Massachusetts, taxation of forests in 166 161 

Mean annual forest per cent 129 114 

Merchantable timber, definition of 167 166 

damages to 140 131 

taxation of 166 162 

Methods of taxation, effect of present condition of forest upon 158 147 

timber estimating, field 218 219 

Mill prices, as a basis of stumpage appraisals 172 171 

Mill run prices, in stumpage appraisals 172 172 

Milling, definition of 90 68 

costs and profits 174 177 



302 INDEX 

Article Page 

Mixed stands, stumpage value for different species in 180 i88 

Money, definition of 2 i 

fluctuating values of, as affecting rate of interest 46 27 

Monopoly, effect of, upon prices and values 7 4 

Moral risks, fire 207 212 

trespass 206 212 

National forest policy, in land classification 250 238 

forests, cost of replacement as basis of damages, on 137 126 

Natural resources, value of 9 5 

Nature of risks in forestry 198 208 

Non-agricultural soils, definition of 232 228 

Normal forest, cost of producing a 109 84 

definition of 109 84 

profit in forestry 107 82 

Operating costs, future, effect on stumpage values 190 201 

Opportunity, economic 27 16 

limitation of 50 29 

Outlay 6 3 

classification of, in accounts 21 13 

permanent, in forestry 93 71 

past, independence of capital value 68 44 

purpose of 20 11 

temporary, in forestry 94 71 

and income accounts 21 12 

account, general, in forestry 131 118 

relation in time between 23 14 

Overhead charges 25 16 

distribution of, in lumbering mixed stands 180 188 

Overturn methods of appraising profits in lumbering 177 181 

Overrun 179 187 

Ownership _ 7 3 

Paper pulp, use of wood for 189 200 

Parcels, cost accounts by, versus entire operation 181 193 

Partial loss, immature timber, damages 141 132 

Past outlay or cost, independence of capital value 68 44 

Penalty, taxes paid on cancellation of classification 166 164 

Pennsylvania, taxation of forests in 166 161 

Per cent, current annual forest 129 1 14 

economic, on forest investments 129 112 

of slope for agricultural soil 227 226 

values taken by taxation, Table II 158 149 

mean annual forest 129 1 14 

Period of installation 23 14 

Permanent improvements and equipment, investment in 97 73 

outlay in forestry 93 71 



INDEX 303 

Article Page 

Perpetual rentals, explanation of meaning 86 64 

present, expectation or capital value of 86 62 

Personal factors in determination of agricultural soil 230 227 

Personality, influence of, upon rate of interest 44 26 

Philosophy of accounts, by Charles E. Sprague 73 52 

Physical risks, definition of 198 197 

fire 200 209 

fungous diseases 203 211 

insects 202 211 

wind 201 210 

separation of timber from soil 133 122 

Pine needles, inflammability 200 210 

Potential income 73 48 

Present condition of forest, efi'ect upon methods of taxation 158 147 

value of future sums 77 54 

perpetual rentals 86 62 

temporary annual rentals 81 58 

intermittent rentals 83 60 

Price basis in appraisals 172 1 70 

changes in forest products 188 197 

general price changes affecting stumpage values 187 197 

levels, changes in prices of forest products 188 197 

Prices, definition 3 2 

for grades of limiber, as basis of stumpage appraisals 172 171 

future, and values, uncertainty of 63 41 

of finished products 8 4 

raw materials and natural resources 9 5 

stumpage 169 167 

factors determining 170 167 

Principles underlying appraisal of damages 133 1 20 

Private measures for control of fire risks 211 214 

versus public forestry, profits in ^ 130 115 

Problem of the balance sheet 73 46 

interest, the 35 20 

in forest taxation 157 146 

taxation for timber lands 155 145 

Products, improvement in quahty of 184 196 

tax 162 152 

Profit and loss account, form for 73 50 

in forestry 131 118 

accounts 21 12 

enterpriser's 39 23 

in lumbering, investment basis of 178 184 

Profits as a per cent of logging and milling costs 177 182 

margin between sale value of lumber, and costs 177 184 

sale value of lumber 177 183 

annual 40 23 

anticipated, on young timber 124 106 



304 INDEX 

Article Page 

Profits, continuous, anticipation of 126 107 

deferred 41 23 

definition of 33 19 

economic 33 19 

expressed as a ratio of income to capital 128 1 10 

expressed in soil values 127 108 

formulas for 246 

from continuous forest production 125 107 

in private versus public forestry 130 115 

destructive lumbering 122 105 

logging 175 179 

lumbering, overturn methods 177 181 

milling '. 174 177 

income versus 42 24 

of logging contractors 177 182 

the undertaking, the 39 23 

on a stand of timber 123 106 

rate of interest in its relation to 121 104 

versus carrj'ing charges on stumpage 181 191 

wages versus 34 19 

Property, definition of ^ 1 i 

tax, forest 159 149 

general 154 144 

general, forest taxes under 164 155 

on value of 151 142 

taxable value of 152 143 

values, effect of taxes on 153 143 

Proprietary accounts 19 11 

in forestry 91 69 

Proprietorship in balance sheet 73 46 

Prospectus or forecast in accounting 73 51 

Protection, expenses for 100 74 

Protective values, damage to 146 137 

Proximate damages 133 121 

Public measures for control of risks 210 213 

policy in regulating private forestry 130 116 

versus private forestry, profits in 130 115 

Punitive damages 147 139 

Purchasers of land, exploitation of 234 229 

Quality of agricultural soil 226 226 

products, improvement in 184 196 

timber, estimation of 223 222 

Railroad assets, valuation of, during construction 57 36 

ties, use of wood for 189 200 

Rate of increase in stumpage value 194 204 

interest, the 38 22 



INDEX 305 

Article Page 

Rate of interest, as affecting damages 139 131 

earned 121 105 

effect of, upon capital value 66 42 

deferred income upon 48 28 

upon accumulations of compound interest 51 30 

, in fores,t.-investments 51 32 

forestry, versus risks 197 208 

its relation to pro6ts 121 104 

influences determining the 43 26 

Rates of interest, in forestry, comparison with other investments 53 ^;i 

Ratio of income or earnings, to investments 89 66 

to capital, profits expressed as 128 no 

Raw materials, prices of 9 5 

material, stumpage as a cost of 176 181 

Reciprocal values in forestry and agriculture 251 239 

Reconnaissance, definition of 55 35 

map 214 217 

Reform, tax, for forest property 166 160 

Regulation of capitalization 72 46 

private forestry by public measures 130 117 

Relative importance of profits in private versus public forestry 130 115 

Relation of rate of interest to profits 121 104 

Rental value, definition of 62 40 

Rentals, definition of 75 53 

Replacement, cost of, basis of damages 137 126 

Reports, stumpage appraisals 224 222 

Resistance of trees to wind 201 210 

Results of simple and compound interest, comparison of 49 28 

Returns on capital 31 18 

Re-valuation of assets 73 48 

Revenue from which to meet taxes, sources of 149 141 

Revision of stumpage values in long term contracts 196 207 

Risk and expense as affecting rate of interest 45 27 

Risks, control of — insurance 209 213 

effect on the business of forest production 212 214 

financial 208 212 

definition of 198 208 

gauging of 199 209 

in forestry, nature of 198 208 

logging 175 179 

moral — trespass 206 212 

— fire 207 212 

physical, definition of 198 208 

— fire 200 209 

— fungous diseases 203 211 

— injurious fumes 205 212 

— insects 202 211 

— wind 201 210 



3o6 INDEX 

Article Page 

Risks, public measures for control of 210 213 

versus rate of interest in forestry 197 208 

Roads and transportation systems, investment in 98 73 

Salaries versus profits 34 19 

Sale value 17 9 

as a basis of damages 138 128 

value 59 37 

effect of capital value upon 69 44 

of agricultural land 238 230 

forest property 245 235 

forests Ill 86 

stump lands 242 232 

stumpage 167 166 

Sales, forced 17 10 

Savings banks, interest rates paid by 53 33 

Scenery, value of 147 139 

Scientific taxation, combined capital tax and income tax 154 163 

forest land tax 160 150 

property tax 159 149 

income or products tax 162 152 

Scope of field appraisals of timber stumpage 213 216 

Sedgwick on damages 133 121 

Sentimental value in damages 133 121 

Separation of timber from soil, physical 135 122 

value of timber from value of soil 136 123 

Services or labor versus investments 22 13 

Shingles, use of 189 199 

Silvicultural operations, cost of 99 74 

Simple interest 16 9 

comparison of results with compound interest 49 28 

Single trees, damage to 144 136 

Slash disposal, cost of 100 74 

Slope, per cent, for agricultural soil 227 226 

Soils, agricultural, definition of 225 226 

Soil, damage to 143 135 

expectation value of 116 92 

quaHty of 226 226 

rent 116 95 

as a cost of growing timber 136 124 

deduction from damages 136 125 

theory of 156 145 

versus forest rent, comparison of taxes on 161 151 

values, profits expressed in 127 108 

Sources of revenue from which to meet taxes 149 141 

Specific accounts 19 11 

in forestry, forms for 131 117 

balance sheet in forestry 120 100 



INDEX 307 

Article Page 

Specific accounts, costs 26 16 

Speculative value 67 43 

Sprague, Charles E., philosophy of accounts 73 52 

Stand, growth in volume of 183 195 

improvement in quality of products 184 196 

Standard log rules 216 219 

of value 2 i 

Standing timber, deterioration of 185 196 

estimation of 215 218 

investment in 96 72 

State forester, power, in enforcing tax laws 166 164 

Strip methods of timber estimating 219 220 

Stump lands, cost of clearing 241 232 

sale value of 242 232 

land versus cleared land 240 231 

Stumpage, carrying charges on, versus profits 181 191 

appraisals, future local supply of timber as affecting 193 204 

local industries and markets 193 204 

reports 224 222 

as a capital investment 176 180 

cost of raw material 176 i8i 

prices 169 167 

factors determining 170 167 

sale value of 168 166 

value, appraisal of 171 169 

rate of increase in 194 204 

values, definition of 167 166 

for different species in mixed stands 180 188 

formulae for 248 

revision of, in long term contracts 196 207 

Substitutes, effect of, on wood prices 189 198 

Summary of elements of value for forest land 243 233 

formulae in forest valuation 243 

of compound interest 240 

Symbols, definition of 241 

Table I — Comparison of Results of Simple and Compound Interest. . . 51 30 

Table II — Comparison of Results of Taxation of Capital Values 158 148 

Table III — Comparison of Sale Value with Expectation Value of 

Even-aged Stand 164 156 

Table IV — Periods within which Property Tax on Timber Becomes 

Equivalent to Tax on Soil Value 165 159 

Table V — Rate of Annual Increase in Value of Stumpage 194 205 

Table VI — Compound Interest Tables 249 

Table VII — Logarithms of Numbers 265 

Tax, general property 154 144 

on income 150 141 

reform for forest property 166 160 



3o8 INDEX 



Article Page 
142 

143 
145 



Tax on value of property 151 

Taxable value of property 152 

Taxation for timber lands, problem of 155 

of forest land bare of timber 166 161 

bearing merchantable timber 166 162 

property in Massachusetts 166 163 

Pennsylvania 166 161 

per cent of values taken by, for forest property 158 149 

scientific, combined capital tax and income tax 163 154 

forest property tax 159 149 

land tax 160 150 

income or products tax 162 152 

Taxes as an expense 103 76 

based on value, not on cost 161 151 

comparison for forests of different age classes, Table II 158 148 

of, on basis of forest rent versus soil rent 161 151 

sources of revenue from which to meet 149 141 

under general property tax 164 155 

Telephone installation, cost of 100 75 

Temporary annual rentals, future value of 79 56 

present, expectation or capital value of 81 58 

intermittent rentals, future value of 82 59 

present, expectation or capital value of 83 60 

outlay in forestry 94 71 

Theory of forest rent 156 146 

soil rent 156 145 

Timber as an agricultural value 239 230 

bonds, security for 96 72 

cost of investments in 106 79 

deterioration of 185 196 

estimates, closeness of utilization as affecting 217 219 

estimating, correction factors 222 221 

errors in methods 219 220 

field methods of 218 219 

quahty of timber 223 222 

reports 224 222 

strip methods 219 220 

use of forest types in 221 221 

estimation of 215 218 

immature, partial loss, damages 141 132 

total loss, damages. T. 142 133 

lands, problem of taxation for 165 145 

merchantable, definition of 167 166 

damage to 140 131 

reconnaissance; the map 214 217 

rights 96 72 

separate from land, value of 119 98 

standing, investment in 96 72 



INDEX 309 

Article Page 

Time, as a factor controlling stumpage prices 170 169 

element in capital value ; 64 42 

of, in values 11 6 

relation in, between outlay and income 23 14 

Total costs, calculation of, in growing timber 105 77 

investment includes working capital 24 15 

loss, immature timber, damages 142 133 

Trading and profit and loss account in forestry 131 1 18 

Transportation costs, effect on stumpage prices 170 169 

effect of methods, upon logging costs 175 178 

facilities, future, as a local factor in stumpage appraisals 190 202 

systems and roads, investments in 98 73 

Trees, damage to 144 136 

Trespass, damage as result of 140 131 

as a moral risk 206 212 

Types, forest, in timber estimating 221 221 

Uncertainty of capital value 67 43 

Undertaking, profits of the 39 23 

Use of logarithms 78 55 

Uses of wood 189 199 

Utilization, closeness of 186 197 

as affecting timber estimates 217 2 19 

Valuation accounts 19 11 

versus specific accounts 54 35 

in forestry 110 85 

of railroad assets during period of construction 57 36 

Value, appraisal of 60 38 

appraised 18 10 

capital, definition of 62 39 

uncertainty of 67 43 

capitalized income, definition of 62 40 

rental, definition of 62 40 

cost as a basis of 56 35 

essential difference between cost and 58 37 

expectation, definition of 62 39 

expenses and interest versus 57 35 

future income as a basis of 61 38 

income, definition of 62 40 

of even-aged forest for any year 115 90 

finished products 4 2 

a forest of even age just previous to cutting 114 89 

forests, income as basis of Ill 85 

forest land, elements of 243 233 

property for continuous forest production 113 88 

destructive lumbering 112 86 

soil 116 92. 



3IO INDEX 

Article Page 

Value of growing stock, even-aged 119 98 

many-aged ■. 119 99 

many-aged forests producing irregular iucome 118 97 

regular income 117 96 

money 2 i 

fluctuating, as aflecting rate of interest 46 27 

property, tax on 151 142 

scenery 147 139 

soil, separation from value of timber 136 1 23 

timber separate from land 119 98 

young timber as part of the value of forest soil 244 234 

rental, definition of 62 40 

sale 17 9 

as a basis of 59 37 

speculative 67 43 

standard of 2 i 

stumpage, definition of 167 166 

appraisal of 171 169 

taxable 152 143 

time element in capital 64 42 

Values 4 2 

aesthetic 147 138 

formulae for 244 

effect of taxes on 153 143 

future, uncertainty of 63 41 

in forestry and agriculture, reciprocal 251 239 

of stumpage for different species in mixed stands 180 188 

Volume growth of stand 183 195 

Wages versus profits 34 19 

Water supply, dependence of agriculture on 229 227 

Watersheds, damage to 146 137 

Wealth 1 r 

Wilful trespass, principle of damages in 140 131 

Wind, as a physical risk 201 210 

Withdrawal of capital 73 49 

Wood prices, effect of substitutes on 189 198 

Wood, uses 189 199 

Woodlot, effect on sale value of farm 138 128 

Woodpeckers 202 211 

Woodworking industries, effect on local stumpage values 192 203 

Working capital 24 15 

Yields per acre, basis of damages 139 130 

Young timber, anticipated profits on 124 106 

value of, as part of the value of forest soil 244 234 



1)0, [To,/ n 



